X381

MIDPOINT OF X2 AND X4

X381 is the point QA-P14 (Centroid of the Morley Triangle) of quadrangle ABCX2 (see http://www.chrisvantienhoven.nl/quadrangle-objects/15-mathematics/quadrangle-objects/artikelen-qa/42-qa-p14.html)
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 4 }: Euler Line { 6, 13 }: Central Line L(6, 13) { 54, 156 }: Central Line L(54, 156) { 127, 133 }: Central Line L(127, 133) { 155, 195 }: Central Line L(155, 195) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_54 = KOSNITA POINT (0.5880, 0.2176) X_156 = -OF-TANGENTIAL-TRIANGLE (0.6520, -0.1707) X_127 = -OF-MEDIAL-TRIANGLE (0.5480, -0.0061) X_133 = INTERSECTION OF LINES X(4)X(74) AND X(5)X(122) (0.5928, 0.5014) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_195 = -CEVA CONJUGATE OF X(3) (0.6761, 0.3331) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) A B C X2 X4 X6 X13 X54 X156 X127 X133 X155 X195 X381 (a, b, c) = (5, 6, 7) | AB = 1

X381 (MIDPOINT OF X2 AND X4) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(2 \cos(B - C) - \cos A : :\)
Barycentrics: \(a(\cos A + 4 \cos B \cos C) : :\)
Search Value (6, 9, 13): \(-1.523625309219\)
▸ Alternate Coordinates7 forms

  • Trilinears: \(\cos A + 4 \cos B \cos C : :\)

  • Trilinears: \(3 \cos A - 4 \sin B \sin C : :\)

  • Trilinears: \((\csc A)(2 \tan A + \tan B + \tan C) + 2 \sec A : :\)

  • Trilinears: \(3 \cos B \cos C + \sin B \sin C : :\)

  • Barycentrics: \(a^{4} - 2b^{4} - 2c^{4} + a^{2}b^{2} + a^{2}c^{2} + 4b^{2}c^{2} : :\)

  • Barycentrics: \(S^{2} + 3 S_{B} S_{C} : :\)

  • Barycentrics: \(a^{2} S_{A} + 4 S_{B} S_{C} : :\)

▸ Linear Combinations2 combinations

  • \(X381) =\) X2 + X4 = X3 + \(2\) X4

  • \(X381) =\) X1 - \(4\) X9955, X1 + \(2\) X18480, X1 + \(5\) X18492, \(2\) X1 - \(5\) X18493, \(2\) X1 + X18525, \(4\) X1 - X18526, X1 - \(5\) X30308, \(7\) X1 - \(4\) X32900, X1 - \(3\) X38021, \(5\) X2 - X20, \(5\) X2 - \(4\) X140, \(4\) X2 + X382, X2 + \(4\) X546, \(3\) X2 - \(4\) X547, \(11\) X2 - \(4\) X548, \(7\) X2 - \(2\) X550, \(7\) X2 - \(5\) X631, \(11\) X2 - \(10\) X632, \(4\) X2 - \(5\) X1656, \(8\) X2 - X1657, \(5\) X2 - \(7\) X3090, X2 - \(5\) X3091, \(7\) X2 + X3146, \(13\) X2 - \(5\) X3522, \(11\) X2 - \(7\) X3523, \(5\) X2 - \(3\) X3524, \(13\) X2 - \(11\) X3525, \(8\) X2 - \(7\) X3526, \(17\) X2 - \(7\) X3528, \(11\) X2 - X3529, \(13\) X2 - \(8\) X3530, \(19\) X2 - \(17\) X3533, \(4\) X2 - X3534, \(3\) X2 + X3543, \(7\) X2 - \(17\) X3544, X2 - \(3\) X3545, \(5\) X2 + \(2\) X3627, \(7\) X2 - \(8\) X3628, \(2\) X2 + X3830, X2 + \(7\) X3832, X2 + \(3\) X3839, \(2\) X2 + \(5\) X3843, X2 + \(2\) X3845, X2 - \(8\) X3850, \(2\) X2 - \(7\) X3851, \(7\) X2 + \(4\) X3853, X2 - \(17\) X3854, X2 - \(11\) X3855, X2 + \(16\) X3856, X2 - \(14\) X3857, X2 + \(10\) X3858, X2 - \(20\) X3859, X2 + \(8\) X3860, \(5\) X2 + \(8\) X3861, \(4\) X2 - \(3\) X5054, \(2\) X2 - \(3\) X5055, \(7\) X2 - \(11\) X5056, \(17\) X2 - X5059, X2 - \(4\) X5066, \(11\) X2 - \(13\) X5067, \(5\) X2 - \(13\) X5068, \(10\) X2 - \(11\) X5070, \(3\) X2 - \(5\) X5071, \(4\) X2 - \(11\) X5072, \(10\) X2 + X5073, \(8\) X2 + \(5\) X5076, \(8\) X2 - \(13\) X5079, \(13\) X2 - \(17\) X7486, \(5\) X2 - \(2\) X8703, \(5\) X2 - \(8\) X10109, \(9\) X2 - \(8\) X10124, \(23\) X2 - \(13\) X10299, \(17\) X2 - \(13\) X10303, \(7\) X2 - \(3\) X10304, \(7\) X2 - X11001, \(7\) X2 - \(6\) X11539, \(19\) X2 - \(16\) X11540, \(25\) X2 + X11541, \(3\) X2 - \(8\) X11737, \(11\) X2 - \(8\) X11812, \(7\) X2 - \(4\) X12100, \(5\) X2 + \(4\) X12101, \(11\) X2 + \(8\) X12102, \(17\) X2 - \(4\) X12103, \(23\) X2 - \(16\) X12108, \(5\) X2 - \(16\) X12811, \(13\) X2 - \(20\) X12812, \(12\) X2 - \(5\) X14093, \(2\) X2 + \(3\) X14269, \(19\) X2 - \(14\) X14869, \(31\) X2 - \(24\) X14890, \(15\) X2 - \(8\) X14891, \(5\) X2 - \(12\) X14892, \(3\) X2 + \(4\) X14893, \(11\) X2 - \(19\) X15022, \(11\) X2 + X15640, \(6\) X2 - X15681, \(5\) X2 + X15682, \(9\) X2 - X15683, \(6\) X2 + X15684, \(10\) X2 - X15685, \(9\) X2 - \(2\) X15686, \(3\) X2 + \(2\) X15687, \(8\) X2 - \(3\) X15688, \(10\) X2 - \(3\) X15689, \(13\) X2 - \(4\) X15690, \(15\) X2 - \(4\) X15691, \(9\) X2 - \(5\) X15692, \(8\) X2 - \(5\) X15693, \(6\) X2 - \(5\) X15694, \(14\) X2 - \(5\) X15695, \(16\) X2 - \(5\) X15696, \(17\) X2 - \(5\) X15697, \(13\) X2 - \(7\) X15698, \(5\) X2 - \(6\) X15699, \(12\) X2 - \(7\) X15700, \(10\) X2 - \(7\) X15701, \(9\) X2 - \(7\) X15702, \(6\) X2 - \(7\) X15703, \(13\) X2 - \(2\) X15704, \(17\) X2 - \(9\) X15705, \(16\) X2 - \(9\) X15706, \(14\) X2 - \(9\) X15707, \(13\) X2 - \(9\) X15708, \(11\) X2 - \(9\) X15709, \(19\) X2 - \(9\) X15710, \(19\) X2 - \(10\) X15711, \(17\) X2 - \(10\) X15712, \(13\) X2 - \(10\) X15713, \(21\) X2 - \(10\) X15714, \(21\) X2 - \(11\) X15715, \(20\) X2 - \(11\) X15716, \(19\) X2 - \(11\) X15717, \(18\) X2 - \(11\) X15718, \(17\) X2 - \(11\) X15719, \(16\) X2 - \(11\) X15720, \(15\) X2 - \(11\) X15721, \(26\) X2 - \(17\) X15722, \(12\) X2 - \(11\) X15723, \(17\) X2 - \(8\) X15759, \(17\) X2 - \(16\) X16239, \(11\) X2 - \(6\) X17504, \(19\) X2 - \(5\) X17538, \(11\) X2 + \(5\) X17578, \(14\) X2 - X17800, \(11\) X2 - \(5\) X19708, \(2\) X2 - \(5\) X19709, \(11\) X2 - \(2\) X19710, \(23\) X2 - \(14\) X19711, \(29\) X2 - \(13\) X21734, \(25\) X2 - \(11\) X21735, X2 + \(6\) X23046, \(7\) X2 + \(2\) X33699, \(13\) X2 + X33703, \(19\) X2 - \(8\) X33923, \(9\) X2 - \(4\) X34200, \(11\) X2 - \(16\) X35018, \(64\) X2 - \(55\) X35381, \(36\) X2 - \(65\) X35382, \(64\) X2 + \(5\) X35384, \(18\) X2 + X35400, \(18\) X2 + \(11\) X35401, \(24\) X2 + \(13\) X35402, \(6\) X2 + \(5\) X35403, \(9\) X2 + \(2\) X35404, \(128\) X2 + \(11\) X35405, \(154\) X2 + \(13\) X35406, \(62\) X2 + \(5\) X35407, \(63\) X2 + \(4\) X35408, \(31\) X2 + \(3\) X35409, \(180\) X2 - \(11\) X35410, \(210\) X2 - \(13\) X35411, \(186\) X2 - \(13\) X35412, \(189\) X2 - \(16\) X35413, \(93\) X2 - \(5\) X35414, \(646\) X2 - \(143\) X35415, \(178\) X2 + \(55\) X35416, \(57\) X2 + \(176\) X35417, \(89\) X2 - \(33\) X35418, \(302\) X2 + \(65\) X35419, \(133\) X2 + \(234\) X35420, \(151\) X2 - \(52\) X35421, \(12\) X2 + \(5\) X35434, \(192\) X2 - \(13\) X35435, X2 - \(6\) X38071, \(4\) X2 + \(3\) X38335, X2 + \(5\) X41099, X2 - \(7\) X41106, \(47\) X2 - \(16\) X41981, \(29\) X2 - \(12\) X41982, \(19\) X2 - \(12\) X41983, \(25\) X2 - \(24\) X41984, \(23\) X2 - \(24\) X41985, \(25\) X2 - \(48\) X41986, \(5\) X2 + \(12\) X41987, \(15\) X2 + \(16\) X41988, \(17\) X2 - \(40\) X41989, \(5\) X2 - \(26\) X41990, X2 + \(22\) X41991, \(47\) X2 - \(46\) X41992, \(25\) X2 - \(8\) X44245, \(25\) X2 - \(16\) X44580, \(25\) X2 - \(14\) X44682, \(15\) X2 - \(2\) X44903, \(17\) X2 - \(28\) X44904, \(17\) X2 - \(24\) X45757, \(55\) X2 - \(48\) X45758, \(13\) X2 - \(6\) X45759, \(47\) X2 - \(40\) X45760, \(99\) X2 - \(56\) X45761, \(15\) X2 + \(28\) X45762, \(14\) X2 - \(13\) X46219, \(37\) X2 - \(16\) X46332, \(17\) X2 - \(3\) X46333, \(23\) X2 - \(10\) X46853, \(25\) X2 - \(29\) X46935, \(19\) X2 - \(23\) X46936, X3 + \(2\) X4, X3 - \(4\) X5, \(5\) X3 - \(2\) X20, \(5\) X3 - \(8\) X140, \(3\) X3 - \(2\) X376, \(2\) X3 + X382, X3 + \(8\) X546, \(3\) X3 - \(8\) X547, \(11\) X3 - \(8\) X548, \(3\) X3 - \(4\) X549, \(7\) X3 - \(4\) X550, \(7\) X3 - \(10\) X631, \(11\) X3 - \(20\) X632, \(2\) X3 - \(5\) X1656, \(4\) X3 - X1657, \(5\) X3 - \(14\) X3090, X3 - \(10\) X3091, \(7\) X3 + \(2\) X3146, \(13\) X3 - \(10\) X3522, \(11\) X3 - \(14\) X3523, \(5\) X3 - \(6\) X3524, \(13\) X3 - \(22\) X3525, \(4\) X3 - \(7\) X3526, \(17\) X3 - \(14\) X3528, \(11\) X3 - \(2\) X3529, \(13\) X3 - \(16\) X3530, \(19\) X3 - \(34\) X3533, \(3\) X3 + \(2\) X3543, \(7\) X3 - \(34\) X3544, X3 - \(6\) X3545, \(5\) X3 + \(4\) X3627, \(7\) X3 - \(16\) X3628, X3 + \(14\) X3832, X3 + \(6\) X3839, X3 + \(5\) X3843, X3 + \(4\) X3845, X3 - \(16\) X3850, X3 - \(7\) X3851, \(7\) X3 + \(8\) X3853, X3 - \(34\) X3854, X3 - \(22\) X3855, X3 + \(32\) X3856, X3 - \(28\) X3857, X3 + \(20\) X3858, X3 - \(40\) X3859, X3 + \(16\) X3860, \(5\) X3 + \(16\) X3861, \(2\) X3 - \(3\) X5054, X3 - \(3\) X5055, \(7\) X3 - \(22\) X5056, \(17\) X3 - \(2\) X5059, X3 - \(8\) X5066, \(11\) X3 - \(26\) X5067, \(5\) X3 - \(26\) X5068, \(5\) X3 - \(11\) X5070, \(3\) X3 - \(10\) X5071, \(2\) X3 - \(11\) X5072, \(5\) X3 + X5073, \(4\) X3 + \(5\) X5076, \(4\) X3 - \(13\) X5079, \(13\) X3 - \(34\) X7486, \(5\) X3 - \(4\) X8703, \(5\) X3 - \(16\) X10109, \(9\) X3 - \(16\) X10124, \(23\) X3 - \(26\) X10299, \(17\) X3 - \(26\) X10303, \(7\) X3 - \(6\) X10304, \(7\) X3 - \(2\) X11001, \(7\) X3 - \(12\) X11539, \(19\) X3 - \(32\) X11540, \(25\) X3 + \(2\) X11541, \(3\) X3 - \(16\) X11737, \(11\) X3 - \(16\) X11812, \(7\) X3 - \(8\) X12100, \(5\) X3 + \(8\) X12101, \(11\) X3 + \(16\) X12102, \(17\) X3 - \(8\) X12103, \(23\) X3 - \(32\) X12108, \(5\) X3 - \(32\) X12811, \(13\) X3 - \(40\) X12812, \(6\) X3 - \(5\) X14093, X3 + \(3\) X14269, \(19\) X3 - \(28\) X14869, \(31\) X3 - \(48\) X14890, \(15\) X3 - \(16\) X14891, \(5\) X3 - \(24\) X14892, \(3\) X3 + \(8\) X14893, \(11\) X3 - \(38\) X15022, \(11\) X3 + \(2\) X15640, \(3\) X3 - X15681, \(5\) X3 + \(2\) X15682, \(9\) X3 - \(2\) X15683, \(3\) X3 + X15684, \(5\) X3 - X15685, \(9\) X3 - \(4\) X15686, \(3\) X3 + \(4\) X15687, \(4\) X3 - \(3\) X15688, \(5\) X3 - \(3\) X15689, \(13\) X3 - \(8\) X15690, \(15\) X3 - \(8\) X15691, \(9\) X3 - \(10\) X15692, \(4\) X3 - \(5\) X15693, \(3\) X3 - \(5\) X15694, \(7\) X3 - \(5\) X15695, \(8\) X3 - \(5\) X15696, \(17\) X3 - \(10\) X15697, \(13\) X3 - \(14\) X15698, \(5\) X3 - \(12\) X15699, \(6\) X3 - \(7\) X15700, \(5\) X3 - \(7\) X15701, \(9\) X3 - \(14\) X15702, \(3\) X3 - \(7\) X15703, \(13\) X3 - \(4\) X15704, \(17\) X3 - \(18\) X15705, \(8\) X3 - \(9\) X15706, \(7\) X3 - \(9\) X15707, \(13\) X3 - \(18\) X15708, \(11\) X3 - \(18\) X15709, \(19\) X3 - \(18\) X15710, \(19\) X3 - \(20\) X15711, \(17\) X3 - \(20\) X15712, \(13\) X3 - \(20\) X15713, \(21\) X3 - \(20\) X15714, \(21\) X3 - \(22\) X15715, \(10\) X3 - \(11\) X15716, \(19\) X3 - \(22\) X15717, \(9\) X3 - \(11\) X15718, \(17\) X3 - \(22\) X15719, \(8\) X3 - \(11\) X15720, \(15\) X3 - \(22\) X15721, \(13\) X3 - \(17\) X15722, \(6\) X3 - \(11\) X15723, \(17\) X3 - \(16\) X15759, \(17\) X3 - \(32\) X16239, \(11\) X3 - \(12\) X17504, \(19\) X3 - \(10\) X17538, \(11\) X3 + \(10\) X17578, \(7\) X3 - X17800, \(11\) X3 - \(10\) X19708, X3 - \(5\) X19709, \(11\) X3 - \(4\) X19710, \(23\) X3 - \(28\) X19711, \(29\) X3 - \(26\) X21734, \(25\) X3 - \(22\) X21735, X3 + \(12\) X23046, \(7\) X3 + \(4\) X33699, \(13\) X3 + \(2\) X33703, \(19\) X3 - \(16\) X33923, \(9\) X3 - \(8\) X34200, \(11\) X3 - \(32\) X35018, \(32\) X3 - \(55\) X35381, \(18\) X3 - \(65\) X35382, \(32\) X3 + \(5\) X35384, \(9\) X3 + X35400, \(9\) X3 + \(11\) X35401, \(12\) X3 + \(13\) X35402, \(3\) X3 + \(5\) X35403, \(9\) X3 + \(4\) X35404, \(64\) X3 + \(11\) X35405, \(77\) X3 + \(13\) X35406, \(31\) X3 + \(5\) X35407, \(63\) X3 + \(8\) X35408, \(31\) X3 + \(6\) X35409, \(90\) X3 - \(11\) X35410, \(105\) X3 - \(13\) X35411, \(93\) X3 - \(13\) X35412, \(189\) X3 - \(32\) X35413, \(93\) X3 - \(10\) X35414, \(323\) X3 - \(143\) X35415, \(89\) X3 + \(55\) X35416, \(57\) X3 + \(352\) X35417, \(89\) X3 - \(66\) X35418, \(151\) X3 + \(65\) X35419, \(133\) X3 + \(468\) X35420, \(151\) X3 - \(104\) X35421, \(6\) X3 + \(5\) X35434, \(96\) X3 - \(13\) X35435, X3 - \(12\) X38071, \(2\) X3 + \(3\) X38335, X3 + \(10\) X41099, X3 - \(14\) X41106, \(47\) X3 - \(32\) X41981, \(29\) X3 - \(24\) X41982, \(19\) X3 - \(24\) X41983, \(25\) X3 - \(48\) X41984, \(23\) X3 - \(48\) X41985, \(25\) X3 - \(96\) X41986, \(5\) X3 + \(24\) X41987, \(15\) X3 + \(32\) X41988, \(17\) X3 - \(80\) X41989, \(5\) X3 - \(52\) X41990, X3 + \(44\) X41991, \(47\) X3 - \(92\) X41992, \(25\) X3 - \(16\) X44245, \(25\) X3 - \(32\) X44580, \(25\) X3 - \(28\) X44682, \(15\) X3 - \(4\) X44903, \(17\) X3 - \(56\) X44904, \(17\) X3 - \(48\) X45757, \(55\) X3 - \(96\) X45758, \(13\) X3 - \(12\) X45759, \(47\) X3 - \(80\) X45760, \(99\) X3 - \(112\) X45761, \(15\) X3 + \(56\) X45762, \(7\) X3 - \(13\) X46219, \(37\) X3 - \(32\) X46332, \(17\) X3 - \(6\) X46333, \(23\) X3 - \(20\) X46853, \(25\) X3 - \(58\) X46935, \(19\) X3 - \(46\) X46936, X4 + \(2\) X5, \(5\) X4 + X20, \(5\) X4 + \(4\) X140, \(3\) X4 + X376, \(4\) X4 - X382, X4 - \(4\) X546, \(3\) X4 + \(4\) X547, \(11\) X4 + \(4\) X548, \(3\) X4 + \(2\) X549, \(7\) X4 + \(2\) X550, \(7\) X4 + \(5\) X631, \(11\) X4 + \(10\) X632, \(4\) X4 + \(5\) X1656, \(8\) X4 + X1657, \(5\) X4 + \(7\) X3090, X4 + \(5\) X3091, \(7\) X4 - X3146, \(13\) X4 + \(5\) X3522, \(11\) X4 + \(7\) X3523, \(5\) X4 + \(3\) X3524, \(13\) X4 + \(11\) X3525, \(8\) X4 + \(7\) X3526, \(17\) X4 + \(7\) X3528, \(11\) X4 + X3529, \(13\) X4 + \(8\) X3530, \(19\) X4 + \(17\) X3533, \(4\) X4 + X3534, \(3\) X4 - X3543, \(7\) X4 + \(17\) X3544, X4 + \(3\) X3545, \(5\) X4 - \(2\) X3627, \(7\) X4 + \(8\) X3628, X4 - \(7\) X3832, X4 - \(3\) X3839, \(2\) X4 - \(5\) X3843, X4 + \(8\) X3850, \(2\) X4 + \(7\) X3851, \(7\) X4 - \(4\) X3853, X4 + \(17\) X3854, X4 + \(11\) X3855, X4 - \(16\) X3856, X4 + \(14\) X3857, X4 - \(10\) X3858, X4 + \(20\) X3859, X4 - \(8\) X3860, \(5\) X4 - \(8\) X3861, \(4\) X4 + \(3\) X5054, \(2\) X4 + \(3\) X5055, \(7\) X4 + \(11\) X5056, \(17\) X4 + X5059, X4 + \(4\) X5066, \(11\) X4 + \(13\) X5067, \(5\) X4 + \(13\) X5068, \(10\) X4 + \(11\) X5070, \(3\) X4 + \(5\) X5071, \(4\) X4 + \(11\) X5072, \(10\) X4 - X5073, \(8\) X4 - \(5\) X5076, \(8\) X4 + \(13\) X5079, \(13\) X4 + \(17\) X7486, \(5\) X4 + \(2\) X8703, \(5\) X4 + \(8\) X10109, \(9\) X4 + \(8\) X10124, \(23\) X4 + \(13\) X10299, \(17\) X4 + \(13\) X10303, \(7\) X4 + \(3\) X10304, \(7\) X4 + X11001, \(7\) X4 + \(6\) X11539, \(19\) X4 + \(16\) X11540, \(25\) X4 - X11541, \(3\) X4 + \(8\) X11737, \(11\) X4 + \(8\) X11812, \(7\) X4 + \(4\) X12100, \(5\) X4 - \(4\) X12101, \(11\) X4 - \(8\) X12102, \(17\) X4 + \(4\) X12103, \(23\) X4 + \(16\) X12108, \(5\) X4 + \(16\) X12811, \(13\) X4 + \(20\) X12812, \(12\) X4 + \(5\) X14093, \(2\) X4 - \(3\) X14269, \(19\) X4 + \(14\) X14869, \(31\) X4 + \(24\) X14890, \(15\) X4 + \(8\) X14891, \(5\) X4 + \(12\) X14892, \(3\) X4 - \(4\) X14893, \(11\) X4 + \(19\) X15022, \(11\) X4 - X15640, \(6\) X4 + X15681, \(5\) X4 - X15682, \(9\) X4 + X15683, \(6\) X4 - X15684, \(10\) X4 + X15685, \(9\) X4 + \(2\) X15686, \(3\) X4 - \(2\) X15687, \(8\) X4 + \(3\) X15688, \(10\) X4 + \(3\) X15689, \(13\) X4 + \(4\) X15690, \(15\) X4 + \(4\) X15691, \(9\) X4 + \(5\) X15692, \(8\) X4 + \(5\) X15693, \(6\) X4 + \(5\) X15694, \(14\) X4 + \(5\) X15695, \(16\) X4 + \(5\) X15696, \(17\) X4 + \(5\) X15697, \(13\) X4 + \(7\) X15698, \(5\) X4 + \(6\) X15699, \(12\) X4 + \(7\) X15700, \(10\) X4 + \(7\) X15701, \(9\) X4 + \(7\) X15702, \(6\) X4 + \(7\) X15703, \(13\) X4 + \(2\) X15704, \(17\) X4 + \(9\) X15705, \(16\) X4 + \(9\) X15706, \(14\) X4 + \(9\) X15707, \(13\) X4 + \(9\) X15708, \(11\) X4 + \(9\) X15709, \(19\) X4 + \(9\) X15710, \(19\) X4 + \(10\) X15711, \(17\) X4 + \(10\) X15712, \(13\) X4 + \(10\) X15713, \(21\) X4 + \(10\) X15714, \(21\) X4 + \(11\) X15715, \(20\) X4 + \(11\) X15716, \(19\) X4 + \(11\) X15717, \(18\) X4 + \(11\) X15718, \(17\) X4 + \(11\) X15719, \(16\) X4 + \(11\) X15720, \(15\) X4 + \(11\) X15721, \(26\) X4 + \(17\) X15722, \(12\) X4 + \(11\) X15723, \(17\) X4 + \(8\) X15759, \(17\) X4 + \(16\) X16239, \(11\) X4 + \(6\) X17504, \(19\) X4 + \(5\) X17538, \(11\) X4 - \(5\) X17578, \(14\) X4 + X17800, \(11\) X4 + \(5\) X19708, \(2\) X4 + \(5\) X19709, \(11\) X4 + \(2\) X19710, \(23\) X4 + \(14\) X19711, \(29\) X4 + \(13\) X21734, \(25\) X4 + \(11\) X21735, X4 - \(6\) X23046, \(7\) X4 - \(2\) X33699, \(13\) X4 - X33703, \(19\) X4 + \(8\) X33923, \(9\) X4 + \(4\) X34200, \(11\) X4 + \(16\) X35018, \(64\) X4 + \(55\) X35381, \(36\) X4 + \(65\) X35382, \(64\) X4 - \(5\) X35384, \(18\) X4 - X35400, \(18\) X4 - \(11\) X35401, \(24\) X4 - \(13\) X35402, \(6\) X4 - \(5\) X35403, \(9\) X4 - \(2\) X35404, \(128\) X4 - \(11\) X35405, \(154\) X4 - \(13\) X35406, \(62\) X4 - \(5\) X35407, \(63\) X4 - \(4\) X35408, \(31\) X4 - \(3\) X35409, \(180\) X4 + \(11\) X35410, \(210\) X4 + \(13\) X35411, \(186\) X4 + \(13\) X35412, \(189\) X4 + \(16\) X35413, \(93\) X4 + \(5\) X35414, \(646\) X4 + \(143\) X35415, \(178\) X4 - \(55\) X35416, \(57\) X4 - \(176\) X35417, \(89\) X4 + \(33\) X35418, \(302\) X4 - \(65\) X35419, \(133\) X4 - \(234\) X35420, \(151\) X4 + \(52\) X35421, \(12\) X4 - \(5\) X35434, \(192\) X4 + \(13\) X35435, X4 + \(6\) X38071, \(4\) X4 - \(3\) X38335, X4 - \(5\) X41099, X4 + \(7\) X41106, \(47\) X4 + \(16\) X41981, \(29\) X4 + \(12\) X41982, \(19\) X4 + \(12\) X41983, \(25\) X4 + \(24\) X41984, \(23\) X4 + \(24\) X41985, \(25\) X4 + \(48\) X41986, \(5\) X4 - \(12\) X41987, \(15\) X4 - \(16\) X41988, \(17\) X4 + \(40\) X41989, \(5\) X4 + \(26\) X41990, X4 - \(22\) X41991, \(47\) X4 + \(46\) X41992, \(25\) X4 + \(8\) X44245, \(25\) X4 + \(16\) X44580, \(25\) X4 + \(14\) X44682, \(15\) X4 + \(2\) X44903, \(17\) X4 + \(28\) X44904, \(17\) X4 + \(24\) X45757, \(55\) X4 + \(48\) X45758, \(13\) X4 + \(6\) X45759, \(47\) X4 + \(40\) X45760, \(99\) X4 + \(56\) X45761, \(15\) X4 - \(28\) X45762, \(14\) X4 + \(13\) X46219, \(37\) X4 + \(16\) X46332, \(17\) X4 + \(3\) X46333, \(23\) X4 + \(10\) X46853, \(25\) X4 + \(29\) X46935, \(19\) X4 + \(23\) X46936, \(10\) X5 - X20, \(5\) X5 - \(2\) X140, \(6\) X5 - X376, \(8\) X5 + X382, X5 + \(2\) X546, \(3\) X5 - \(2\) X547, \(11\) X5 - \(2\) X548, \(3\) X5 - X549, \(7\) X5 - X550, \(14\) X5 - \(5\) X631, \(11\) X5 - \(5\) X632, \(8\) X5 - \(5\) X1656, \(16\) X5 - X1657, \(10\) X5 - \(7\) X3090, \(2\) X5 - \(5\) X3091, \(14\) X5 + X3146, \(26\) X5 - \(5\) X3522, \(22\) X5 - \(7\) X3523, \(10\) X5 - \(3\) X3524, \(26\) X5 - \(11\) X3525, \(16\) X5 - \(7\) X3526, \(34\) X5 - \(7\) X3528, \(22\) X5 - X3529, \(13\) X5 - \(4\) X3530, \(38\) X5 - \(17\) X3533, \(8\) X5 - X3534, \(6\) X5 + X3543, \(14\) X5 - \(17\) X3544, \(2\) X5 - \(3\) X3545, \(5\) X5 + X3627, \(7\) X5 - \(4\) X3628, \(4\) X5 + X3830, \(2\) X5 + \(7\) X3832, \(2\) X5 + \(3\) X3839, \(4\) X5 + \(5\) X3843, X5 - \(4\) X3850, \(4\) X5 - \(7\) X3851, \(7\) X5 + \(2\) X3853, \(2\) X5 - \(17\) X3854, \(2\) X5 - \(11\) X3855, X5 + \(8\) X3856, X5 - \(7\) X3857, and thousands more

X381 lies on the McCay circumcircle, the curves K300, K358, K504, K649, K762, K833, K887, K911, Q164.

▸ Incident Central Lines1387 lines

{1, 2463}, {2, 3}, {6, 13}, {7, 38073}, {8, 8148}, {9, 18482}, {10, 2467}, {11, 999}, {12, 1479}, {15, 16644}, {16, 16645}, {17, 12817}, {18, 12816}, {19, 18453}, {32, 13881}, {33, 9642}, {34, 18447}, {35, 12953}, {36, 12943}, {39, 2015}, {40, 7989}, {46, 7082}, {49, 578}, {51, 568}, {52, 5907}, {53, 18437}, {54, 156}, {55, 3583}, {56, 3582}, {57, 18540}, {61, 5339}, {62, 5340}, {64, 3521}, {65, 10826}, {67, 32271}, {68, 3527}, {69, 3531}, {74, 1539}, {76, 7773}, {79, 5221}, {80, 2099}, {83, 7851}, {84, 22792}, {90, 1454}, {98, 598}, {99, 22515}, {100, 22938}, {103, 38768}, {104, 22799}, {109, 38780}, {110, 7699}, {111, 6032}, {112, 19163}, {114, 543}, {116, 10741}, {117, 10747}, {118, 544}, {119, 528}, {120, 15521}, {121, 15522}, {122, 22337}, {123, 33566}, {124, 10740}, {125, 541}, {126, 22338}, {127, 133}, {128, 13512}, {130, 38594}, {131, 5139}, {132, 10749}, {137, 31656}, {141, 31670}, {142, 31672}, {143, 5876}, {145, 37705}, {146, 7693}, {147, 12243}, {148, 7777}, {149, 11698}, {153, 1484}, {154, 18376}, {155, 195}, {157, 11641}, {159, 18382}, {165, 11231}, {182, 2469}, {183, 316}, {184, 567}, {185, 5462}, {187, 37637}, {190, 24827}, {206, 34775}, {210, 517}, {216, 33842}, {220, 24045}, {226, 5722}, {230, 1384}, {233, 36751}, {262, 671}, {264, 339}, {275, 19176}, {298, 622}, {299, 621}, {302, 616}, {303, 617}, {315, 37671}, {325, 11185}, {355, 519}, {371, 8976}, {372, 13847}, {373, 5892}, {385, 34623}, {388, 496}, {389, 12162}, {390, 8164}, {393, 15851}, {394, 1568}, {395, 5318}, {396, 5321}, {397, 40694}, {398, 40693}, {485, 1328}, {486, 1327}, {487, 22809}, {488, 22810}, {493, 18520}, {494, 18522}, {495, 497}, {498, 3614}, {499, 5298}, {511, 599}, {512, 13240}, {513, 39483}, {514, 39489}, {515, 551}, {516, 3828}, {523, 16279}, {524, 1351}, {525, 39491}, {527, 2095}, {529, 3829}, {530, 5478}, {531, 5479}, {532, 5858}, {533, 5859}, {535, 11194}, {536, 20430}, {538, 3095}, {540, 7683}, {545, 24828}, {553, 1210}, {569, 6759}, {574, 7603}, {576, 15069}, {590, 6221}, {591, 6250}, {597, 1503}, {615, 6398}, {620, 38730}, {623, 3643}, {624, 3642}, {625, 3734}, {627, 33608}, {628, 33609}, {629, 33619}, {630, 33618}, {637, 32809}, {638, 32808}, {754, 6249}, {804, 19912}, {900, 39493}, {908, 3419}, {912, 5927}, {916, 31163}, {938, 5714}, {942, 1864}, {944, 5901}, {950, 11374}, {952, 3241}, {956, 5080}, {958, 25639}, {960, 16616}, {962, 5690}, {971, 6173}, {986, 5492}, {997, 5087}, {1001, 3822}, {1007, 6390}, {1056, 5274}, {1058, 5261}, {1060, 9817}, {1062, 9641}, {1073, 37873}, {1078, 11057}, {1092, 37495}, {1093, 14860}, {1112, 7723}, {1116, 32478}, {1125, 3653}, {1131, 6501}, {1132, 6500}, {1147, 11424}, {1151, 10576}, {1152, 10577}, {1154, 3060}, {1157, 16764}, {1159, 12019}, {1160, 7721}, {1161, 7720}, {1173, 45014}, {1181, 19361}, {1199, 43605}, {1209, 12307}, {1216, 37484}, {1217, 36609}, {1263, 16762}, {1285, 37689}, {1296, 38800}, {1297, 19160}, {1319, 23708}, {1329, 9709}, {1350, 14926}, {1353, 5032}, {1376, 3814}, {1385, 5691}, {1387, 3476}, {1388, 37735}, {1470, 13273}, {1480, 33104}, {1483, 10595}, {1490, 37615}, {1495, 14805}, {1498, 15047}, {1499, 8371}, {1506, 5013}, {1511, 10546}, {1514, 3426}, {1531, 3581}, {1533, 35237}, {1537, 19914}, {1565, 17079}, {1587, 6418}, {1588, 6417}, {1614, 13434}, {1698, 3579}, {1714, 9958}, {1737, 1836}, {1750, 18443}, {1770, 24914}, {1837, 12047}, {1843, 18438}, {1853, 5943}, {1870, 37729}, {1898, 13750}, {1974, 19129}, {1975, 7752}, {1986, 22584}, {1991, 6251}, {1992, 3564}, {1993, 15068}, {1994, 15052}, {2039, 38597}, {2040, 38596}, {2051, 9567}, {2080, 3849}, {2094, 5770}, {2096, 13226}, {2098, 37710}, {2393, 23049}, {2452, 9214}, {2453, 5099}, {2482, 15561}, {2548, 5254}, {2549, 3815}, {2550, 3820}, {2551, 31418}, {2646, 37692}, {2770, 32229}, {2771, 5902}, {2775, 14431}, {2777, 10606}, {2779, 15049}, {2780, 9148}, {2781, 16776}, {2794, 5461}, {2796, 24311}, {2797, 45319}, {2799, 44203}, {2800, 38161}, {2808, 10708}, {2818, 10709}, {2829, 23513}, {2883, 12315}, {2886, 9708}, {2888, 12316}, {2900, 5720}, {2917, 32365}, {2929, 22816}, {2930, 32273}, {2931, 19479}, {2935, 32743}, {2971, 23635}, {2979, 13391}, {2999, 18505}, {3023, 10054}, {3027, 10070}, {3052, 17734}, {3053, 7746}, {3054, 15655}, {3055, 43619}, {3057, 10827}, {3065, 16763}, {3068, 6199}, {3069, 6395}, {3085, 5225}, {3086, 5229}, {3087, 38292}, {3098, 3763}, {3106, 31702}, {3107, 31701}, {3120, 7986}, {3167, 5654}, {3258, 14685}, {3259, 38586}, {3297, 35800}, {3298, 35801}, {3303, 4857}, {3304, 5270}, {3309, 31149}, {3314, 43453}, {3316, 43567}, {3317, 43566}, {3336, 7701}, {3357, 5895}, {3358, 15239}, {3359, 11372}, {3361, 31776}, {3366, 42236}, {3367, 42238}, {3373, 12823}, {3388, 12822}, {3391, 42235}, {3392, 42237}, {3398, 7817}, {3411, 42533}, {3412, 42532}, {3413, 41880}, {3414, 41881}, {3424, 18842}, {3434, 17757}, {3436, 24390}, {3448, 11801}, {3459, 22335}, {3483, 16765}, {3485, 37730}, {3486, 37737}, {3487, 12433}, {3488, 5226}, {3567, 6102}, {3576, 7988}, {3586, 5219}, {3587, 7308}, {3589, 12017}, {3592, 8960}, {3616, 34773}, {3617, 38081}, {3618, 38079}, {3624, 13624}, {3632, 11278}, {3634, 31730}, {3652, 16125}, {3667, 39490}, {3695, 42032}, {3746, 9670}, {3767, 5306}, {3785, 32885}, {3793, 37667}, {3796, 44407}, {3824, 41854}, {3825, 25524}, {3847, 10200}, {3917, 10170}, {3925, 34618}, {3927, 6734}, {3928, 5789}, {3929, 5709}, {3933, 32816}, {3934, 7784}, {3944, 37717}, {3972, 10722}, {4252, 45939}, {4292, 37545}, {4293, 10589}, {4294, 10588}, {4297, 19883}, {4299, 5433}, {4301, 4669}, {4302, 5432}, {4370, 29243}, {4388, 5774}, {4413, 35238}, {4421, 11496}, {4428, 10197}, {4549, 32269}, {4664, 29010}, {4677, 7982}, {4745, 11362}, {4994, 19210}, {5012, 14157}, {5023, 7749}, {5031, 35456}, {5044, 37585}, {5045, 5290}, {5048, 37708}, {5085, 10168}, {5086, 5730}, {5090, 34713}, {5092, 7913}, {5095, 32272}, {5102, 5965}, {5103, 35458}, {5122, 31231}, {5123, 35460}, {5134, 42316}, {5158, 18487}, {5167, 18322}, {5203, 40809}, {5204, 10483}, {5206, 44535}, {5210, 6781}, {5215, 32414}, {5237, 42431}, {5238, 42432}, {5251, 31245}, {5252, 30384}, {5289, 11813}, {5292, 13408}, {5305, 43136}, {5325, 5791}, {5334, 11542}, {5335, 11543}, {5343, 42494}, {5344, 42495}, {5349, 42147}, {5350, 42148}, {5351, 42491}, {5352, 42490}, {5365, 42925}, {5366, 42924}, {5412, 18457}, {5413, 18459}, {5418, 6449}, {5420, 6450}, {5422, 11456}, {5437, 7171}, {5439, 13369}, {5440, 30852}, {5443, 34471}, {5446, 5562}, {5449, 12163}, {5459, 41022}, {5460, 41023}, {5463, 36765}, {5485, 14484}, {5510, 10744}, {5523, 45141}, {5533, 12763}, {5544, 11820}, {5563, 9657}, {5597, 18495}, {5598, 18497}, {5609, 11422}, {5627, 14254}, {5640, 5663}, {5642, 14643}, {5644, 5656}, {5646, 33544}, {5650, 36987}, {5651, 13857}, {5657, 9812}, {5687, 11681}, {5694, 37625}, {5704, 34753}, {5705, 31445}, {5706, 37509}, {5707, 36750}, {5715, 5777}, {5725, 24210}, {5726, 31393}, {5731, 28186}, {5732, 38093}, {5752, 15488}, {5762, 5817}, {5787, 6260}, {5794, 21616}, {5816, 17330}, {5840, 6174}, {5841, 31157}, {5842, 38109}, {5843, 38137}, {5844, 31145}, {5860, 6201}, {5861, 6202}, {5864, 21359}, {5865, 21360}, {5878, 5893}, {5881, 10222}, {5884, 31871}, {5885, 15071}, {5887, 7686}, {5898, 18427}, {5913, 21448}, {5944, 26882}, {5972, 12121}, {6002, 45665}, {6036, 14971}, {6090, 40112}, {6101, 11444}, {6108, 22513}, {6109, 22512}, {6114, 6775}, {6115, 6772}, {6145, 32364}, {6146, 19347}, {6152, 22815}, {6153, 43581}, {6200, 8253}, {6235, 6324}, {6241, 11439}, {6244, 7965}, {6245, 6259}, {6246, 6265}, {6253, 26487}, {6256, 16203}, {6278, 22485}, {6281, 22484}, {6291, 22811}, {6337, 32826}, {6361, 9780}, {6391, 45088}, {6396, 8252}, {6406, 22812}, {6407, 9540}, {6408, 13935}, {6409, 42266}, {6410, 42267}, {6425, 35730}, {6426, 35813}, {6445, 9541}, {6446, 32786}, {6447, 31454}, {6448, 42418}, {6451, 32789}, {6452, 32790}, {6455, 42260}, {6456, 42261}, {6459, 8981}, {6460, 13966}, {6472, 43520}, {6473, 43519}, {6480, 42558}, {6481, 42557}, {6484, 42568}, {6485, 42569}, {6519, 9681}, {6522, 41964}, {6526, 13157}, {6666, 38067}, {6667, 38069}, {6668, 38070}, {6683, 7872}, {6688, 14855}, {6689, 32340}, {6696, 20427}, {6697, 34778}, {6699, 13202}, {6702, 12515}, {6704, 8725}, {6712, 38765}, {6713, 38753}, {6716, 23240}, {6718, 38777}, {6721, 9167}, {6722, 38739}, {6723, 16111}, {6748, 15905}, {6750, 36245}, {6770, 20252}, {6771, 22489}, {6773, 20253}, {6774, 22490}, {6776, 13674}, {6782, 41745}, {6783, 41746}, {6785, 6787}, {6788, 18326}, {6792, 18346}, {6795, 38393}, {7160, 22801}, {7578, 18300}, {7585, 23273}, {7586, 23267}, {7592, 32139}, {7607, 45103}, {7608, 17503}, {7618, 9771}, {7620, 9770}, {7622, 32479}, {7666, 45248}, {7678, 42884}, {7691, 13565}, {7710, 46034}, {7735, 18907}, {7736, 15048}, {7738, 31404}, {7750, 32832}, {7751, 7843}, {7754, 7785}, {7756, 15815}, {7761, 15271}, {7763, 32819}, {7764, 22665}, {7767, 32006}, {7772, 39593}, {7774, 22253}, {7790, 11174}, {7793, 19569}, {7798, 32457}, {7804, 7844}, {7806, 9862}, {7808, 7861}, {7810, 8556}, {7812, 14568}, {7814, 32821}, {7815, 7842}, {7816, 7862}, {7821, 17130}, {7823, 32151}, {7827, 39646}, {7828, 9873}, {7840, 32515}, {7845, 17131}, {7868, 7934}, {7879, 7885}, {7881, 7912}, {7883, 33706}, {7900, 17129}, {7914, 35248}, {7935, 31239}, {7941, 20081}, {7956, 34625}, {7967, 10283}, {7999, 10627}, {8068, 8069}, {8070, 8071}, {8074, 18327}, {8182, 15597}, {8192, 34668}, {8193, 34657}, {8196, 8200}, {8203, 8207}, {8212, 8220}, {8213, 8221}, {8254, 12254}, {8288, 45723}, {8541, 18449}, {8547, 20113}, {8567, 25563}, {8573, 9722}, {8584, 11482}, {8585, 39602}, {8589, 44541}, {8680, 25362}, {8704, 13377}, {8717, 22112}, {8722, 15810}, {8757, 23070}, {8760, 45320}, {8780, 23292}, {8859, 10788}, {8860, 38227}, {8939, 18414}, {8943, 18415}, {9115, 23006}, {9117, 23013}, {9143, 25147}, {9144, 11005}, {9172, 14666}, {9175, 14684}, {9178, 18309}, {9306, 13352}, {9308, 17035}, {9543, 10145}, {9578, 9614}, {9579, 37582}, {9580, 31434}, {9598, 31460}, {9607, 31417}, {9613, 24928}, {9624, 15178}, {9664, 31476}, {9665, 16781}, {9680, 10195}, {9690, 43508}, {9691, 43512}, {9698, 22332}, {9707, 12289}, {9717, 34150}, {9729, 10575}, {9732, 45481}, {9733, 45480}, {9734, 14162}, {9746, 28897}, {9752, 23055}, {9753, 22329}, {9755, 11177}, {9764, 9765}, {9767, 9768}, {9775, 42008}, {9777, 11442}, {9778, 28178}, {9816, 15941}, {9820, 12118}, {9822, 37511}, {9826, 12133}, {9830, 12177}, {9833, 14530}, {9856, 37562}, {9863, 34604}, {9895, 15940}, {9919, 44883}, {9937, 22661}, {9970, 32274}, {9973, 43129}, {9979, 44204}, {10002, 36876}, {10003, 42329}, {10031, 19907}, {10032, 19919}, {10039, 12701}, {10086, 12354}, {10089, 18969}, {10104, 12110}, {10106, 11373}, {10112, 40240}, {10117, 19506}, {10152, 38605}, {10164, 10172}, {10165, 10171}, {10187, 42505}, {10188, 42504}, {10194, 43562}, {10199, 12114}, {10217, 36299}, {10218, 36298}, {10249, 36201}, {10263, 11017}, {10265, 16112}, {10266, 22805}, {10269, 41698}, {10272, 12383}, {10274, 40276}, {10278, 16220}, {10282, 17845}, {10302, 14488}, {10306, 10525}, {10311, 10317}, {10418, 14653}, {10446, 17271}, {10526, 22770}, {10531, 10599}, {10532, 10598}, {10572, 11375}, {10574, 12006}, {10596, 32213}, {10597, 32214}, {10601, 11550}, {10625, 11793}, {10641, 18468}, {10642, 18470}, {10645, 42096}, {10646, 42097}, {10712, 28915}, {10717, 33962}, {10718, 20410}, {10721, 12041}, {10723, 11164}, {10724, 33814}, {10725, 38599}, {10726, 38600}, {10727, 31273}, {10728, 31272}, {10729, 38603}, {10730, 38604}, {10731, 38606}, {10732, 38607}, {10734, 14650}, {10735, 38608}, {10746, 25640}, {10752, 13169}, {10753, 11161}, {10886, 37620}, {10897, 35764}, {10898, 35765}, {10984, 37471}, {10985, 18472}, {10990, 20397}, {10991, 20398}, {10992, 20399}, {10993, 20400}, {11002, 13451}, {11004, 18387}, {11011, 37711}, {11160, 34380}, {11167, 14485}, {11170, 43535}, {11171, 37808}, {11173, 15993}, {11182, 21733}, {11187, 44420}, {11188, 14984}, {11202, 39242}, {11245, 45967}, {11257, 11272}, {11271, 11803}, {11376, 45287}, {11381, 27355}, {11396, 34729}, {11402, 12022}, {11425, 13403}, {11426, 12134}, {11432, 12233}, {11433, 18917}, {11438, 26958}, {11440, 43613}, {11441, 12161}, {11449, 43394}, {11451, 11455}, {11457, 12174}, {11477, 15533}, {11480, 16241}, {11481, 16242}, {11487, 11850}, {11488, 42117}, {11489, 42118}, {11557, 21650}, {11561, 12270}, {11562, 41671}, {11572, 13353}, {11576, 12606}, {11669, 33698}, {11671, 14072}, {11693, 38795}, {11694, 34153}, {11695, 46850}, {11699, 12407}, {11704, 11999}, {11723, 12898}, {11750, 13419}, {11805, 33565}, {12112, 15018}, {12115, 30283}, {12154, 41060}, {12155, 41061}, {12160, 41628}, {12236, 12825}, {12242, 15752}, {12261, 12368}, {12278, 15807}, {12279, 15028}, {12281, 38898}, {12284, 13358}, {12292, 14708}, {12301, 20302}, {12302, 33547}, {12313, 45861}, {12314, 45860}, {12322, 32811}, {12323, 32810}, {12350, 13183}, {12351, 13182}, {12370, 14516}, {12412, 40914}, {12513, 24387}, {12528, 24475}, {12599, 12856}, {12600, 12919}, {12619, 34789}, {12672, 25413}, {12680, 13373}, {12688, 34339}, {12737, 16174}, {12818, 43569}, {12819, 43568}, {12820, 42629}, {12821, 42630}, {12897, 35602}, {12900, 16163}, {12978, 22817}, {12979, 22818}, {13051, 22813}, {13052, 22814}, {13055, 22821}, {13056, 22822}, {13151, 25525}, {13335, 36997}, {13339, 43650}, {13349, 36994}, {13350, 36992}, {13432, 15801}, {13445, 43584}, {13464, 37727}, {13465, 16159}, {13468, 44678}, {13482, 34148}, {13557, 21268}, {13558, 22823}, {13561, 26917}, {13599, 39284}, {13623, 14490}, {13638, 13644}, {13687, 13692}, {13748, 45411}, {13749, 45410}, {13758, 13763}, {13807, 13812}, {13875, 22641}, {13876, 22640}, {13886, 23275}, {13893, 31439}, {13915, 19060}, {13925, 42639}, {13928, 22612}, {13929, 22611}, {13939, 23269}, {13979, 19059}, {13993, 42640}, {14059, 33546}, {14094, 15019}, {14103, 22752}, {14163, 14214}, {14164, 14215}, {14249, 14978}, {14260, 36590}, {14385, 45694}, {14389, 26864}, {14457, 38260}, {14483, 19307}, {14494, 41895}, {14528, 17505}, {14583, 14993}, {14635, 32428}, {14647, 38159}, {14663, 42425}, {14677, 40685}, {14686, 38588}, {14693, 26613}, {14712, 17004}, {14731, 18319}, {14833, 21460}, {14861, 22334}, {14866, 31749}, {14907, 37688}, {14929, 15589}, {14961, 33843}, {14980, 46439}, {14981, 38734}, {14989, 38610}, {15017, 22935}, {15025, 20396}, {15027, 16003}, {15032, 34545}, {15039, 30714}, {15054, 20379}, {15055, 34128}, {15063, 36253}, {15066, 37496}, {15107, 33533}, {15111, 16168}, {15252, 34231}, {15310, 31151}, {15311, 23332}, {15317, 22466}, {15356, 18114}, {15392, 38539}, {15436, 22555}, {15475, 18308}, {15535, 15542}, {15536, 15541}, {15538, 15544}, {15539, 15545}, {15548, 15549}, {15551, 15552}, {15740, 45073}, {15806, 43818}, {15811, 37514}, {15817, 15833}, {15873, 41587}, {15922, 34113}, {16001, 35752}, {16002, 36330}, {16010, 20301}, {16118, 26202}, {16188, 38582}, {16200, 34747}, {16202, 18242}, {16228, 44923}, {16229, 44918}, {16230, 44921}, {16231, 44925}, {16264, 17907}, {16318, 41370}, {16336, 35449}, {16337, 19552}, {16466, 21935}, {16509, 23334}, {16534, 23236}, {16772, 42150}, {16773, 42151}, {16835, 43585}, {16960, 44016}, {16961, 44015}, {17078, 17181}, {17254, 29369}, {17310, 29331}, {17313, 24220}, {17500, 43917}, {17502, 28168}, {17508, 29323}, {17647, 25681}, {17810, 21243}, {17811, 37483}, {17813, 23048}, {17814, 36747}, {17821, 34785}, {18201, 31520}, {18230, 38082}, {18279, 32417}, {18310, 44206}, {18321, 31850}, {18395, 37567}, {18402, 38585}, {18432, 34117}, {18442, 46027}, {18462, 19446}, {18463, 19447}, {18549, 22836}, {18576, 18883}, {18809, 38595}, {18911, 32111}, {18912, 32140}, {18945, 31804}, {19132, 34776}, {19177, 19189}, {19357, 21659}, {19722, 31872}, {19765, 37693}, {20192, 44569}, {20401, 33520}, {20415, 41020}, {20416, 41021}, {20546, 35462}, {20576, 36998}, {20582, 29181}, {20584, 21230}, {21151, 38171}, {21153, 38318}, {21154, 38319}, {21356, 40330}, {21635, 33594}, {22235, 33603}, {22237, 33602}, {22240, 33885}, {22246, 37665}, {22247, 38731}, {22550, 44686}, {22573, 22579}, {22574, 22580}, {22691, 22707}, {22692, 22708}, {22712, 31168}, {22808, 22970}, {22833, 22955}, {22846, 36760}, {22847, 22861}, {22848, 22862}, {22891, 36759}, {22892, 22906}, {22893, 22907}, {22971, 37497}, {23017, 25178}, {23018, 25183}, {23019, 25184}, {23020, 25185}, {23021, 25186}, {23022, 25220}, {23023, 25173}, {23024, 25187}, {23025, 25188}, {23026, 25189}, {23027, 25190}, {23028, 25219}, {23071, 34048}, {23294, 43807}, {23302, 42085}, {23303, 42086}, {23878, 33752}, {24042, 34626}, {24441, 29069}, {24466, 38762}, {24931, 46975}, {24953, 35250}, {25175, 25223}, {25180, 25224}, {25406, 38110}, {25423, 44823}, {26098, 37715}, {26326, 26386}, {26327, 26410}, {26328, 26466}, {26329, 26467}, {26363, 35252}, {26364, 35251}, {28212, 38112}, {28228, 38127}, {28234, 34641}, {29317, 31884}, {29365, 44430}, {30143, 33858}, {30209, 31174}, {30212, 45686}, {30258, 39530}, {30311, 45043}, {30484, 32536}, {30522, 35264}, {31274, 38736}, {31383, 37649}, {31399, 43174}, {31423, 31663}, {31428, 31430}, {31441, 31443}, {31466, 31468}, {31472, 31474}, {31484, 31485}, {31488, 31490}, {31492, 31652}, {31655, 38598}, {31657, 36991}, {31748, 46673}, {31793, 31822}, {31803, 31870}, {31824, 32156}, {31827, 34795}, {31841, 38584}, {31860, 32223}, {32152, 34506}, {32196, 32338}, {32267, 41424}, {32369, 32379}, {32445, 41334}, {32533, 43908}, {32599, 37827}, {32612, 37001}, {32613, 36999}, {32822, 32831}, {32823, 32830}, {32825, 32896}, {32869, 37668}, {33106, 37716}, {33416, 42100}, {33417, 42099}, {33531, 34286}, {33540, 33542}, {33586, 37494}, {33592, 37702}, {33596, 34701}, {33604, 43207}, {33605, 43208}, {33606, 42521}, {33607, 42520}, {33884, 44324}, {33971, 37765}, {34126, 38693}, {34127, 34473}, {34169, 45143}, {34170, 41372}, {34175, 36822}, {34360, 35088}, {34573, 43621}, {34699, 37725}, {34719, 37622}, {34754, 43782}, {34755, 43781}, {34799, 45970}, {34836, 41244}, {34842, 38956}, {34845, 43919}, {34897, 40801}, {34945, 39524}, {35194, 37591}, {35514, 38092}, {35698, 35879}, {35699, 35878}, {35719, 42441}, {36441, 36460}, {36442, 36459}, {36451, 36461}, {36523, 38745}, {36742, 45931}, {36755, 40334}, {36756, 40335}, {36764, 36772}, {36836, 42157}, {36843, 42158}, {36971, 41700}, {37487, 44673}, {37512, 44519}, {37529, 42043}, {37699, 42042}, {37726, 38757}, {37809, 44401}, {37810, 38226}, {38025, 43161}, {38094, 43182}, {38104, 46684}, {38609, 44967}, {38611, 44969}, {38612, 44970}, {38613, 44972}, {38614, 44973}, {38615, 44976}, {38616, 44977}, {38617, 44979}, {38618, 44981}, {38619, 44983}, {38620, 44984}, {38621, 44985}, {38622, 44986}, {38623, 44987}, {38624, 44988}, {38625, 44992}, {38723, 38793}, {38727, 38788}, {38737, 38742}, {38797, 40556}, {38947, 45146}, {38952, 45145}, {39201, 39510}, {39529, 39531}, {39532, 44928}, {39533, 44931}, {39534, 44929}, {39535, 44927}, {39536, 44930}, {39561, 45730}, {39818, 39828}, {39847, 39857}, {40286, 45484}, {40287, 45485}, {40671, 41045}, {40672, 41044}, {40879, 46996}, {41095, 41097}, {41096, 41123}, {41116, 41126}, {41311, 46475}, {41714, 44439}, {41953, 43323}, {41954, 43322}, {41961, 41967}, {41962, 41968}, {41971, 42892}, {41972, 42893}, {41973, 42976}, {41974, 42977}, {42087, 42092}, {42088, 42089}, {42090, 42108}, {42091, 42109}, {42112, 42500}, {42113, 42501}, {42119, 42124}, {42120, 42121}, {42122, 42140}, {42123, 42141}, {42144, 42984}, {42145, 42985}, {42175, 42182}, {42176, 42180}, {42177, 42181}, {42178, 42179}, {42435, 43551}, {42436, 43550}, {42496, 42633}, {42497, 42634}, {42506, 42991}, {42507, 42990}, {42512, 42688}, {42513, 42689}, {42518, 42635}, {42519, 42636}, {42566, 43337}, {42567, 43336}, {42570, 43341}, {42571, 43340}, {42572, 43343}, {42573, 43342}, {42588, 43109}, {42589, 43108}, {42610, 43369}, {42611, 43368}, {42612, 42961}, {42613, 42960}, {42627, 43466}, {42628, 43465}, {42645, 42727}, {42646, 42728}, {42682, 43105}, {42683, 43106}, {42692, 42777}, {42693, 42778}, {42694, 42939}, {42695, 42938}, {42725, 46473}, {42726, 46476}, {42775, 42999}, {42776, 42998}, {42791, 42945}, {42792, 42944}, {42795, 42955}, {42796, 42954}, {42799, 43332}, {42800, 43333}, {42888, 43463}, {42889, 43464}, {42904, 43004}, {42905, 43005}, {42908, 42979}, {42909, 42978}, {42922, 42987}, {42923, 42986}, {43006, 43233}, {43007, 43232}, {43010, 43014}, {43011, 43015}, {43012, 43019}, {43013, 43018}, {43195, 43241}, {43196, 43240}, {43197, 43243}, {43198, 43242}, {43203, 43249}, {43204, 43248}, {43205, 43251}, {43206, 43250}, {43278, 43389}, {43292, 43549}, {43293, 43548}, {43364, 43777}, {43365, 43778}, {43415, 43507}, {43467, 43636}, {43468, 43637}, {43469, 43641}, {43470, 43642}, {43471, 43490}, {43472, 43489}, {43473, 43494}, {43474, 43493}, {43479, 43502}, {43480, 43501}, {43511, 43521}, {43515, 43525}, {43516, 43526}, {43536, 43561}, {43575, 45731}, {43592, 44801}, {43699, 44731}, {44202, 44564}, {44469, 45034}, {44666, 45879}, {44667, 45880}, {45811, 45821}, {46633, 46977}, {46634, 46979}, {46980, 46988}, {46982, 46986}

▸ Functional Relations62 relations

  • X381 = midpoint of Xi and Xj for these {i,j}: {2, 4}, {3, 3830}, {5, 3845}, {13, 41042}, {14, 41043}, {20, 15682}, {51, 15030}, {114, 9880}, {140, 12101}, {147, 12243}, {154, 18405}, {265, 5655}, {355, 3656}, {376, 3543}, {382, 3534}, {428, 34664}, {546, 5066}, {547, 14893}, {549, 15687}, {550, 33699}, {551, 34648}, {568, 18435}, {598, 10033}, {671, 6054}, {1352, 20423}, {1513, 8352}, {1531, 32225}, {1551, 36196}, {1699, 5587}, {1992, 11180}, {3058, 34746}, {3060, 11459}, {3091, 41099}, {3146, 11001}, {3241, 34627}, {3426, 44750}, {3529, 15640}, {3545, 3839}, {3627, 8703}, {3654, 12699}, {3679, 31162}, {3818, 5476}, {3832, 41106}, {3843, 19709}, {3850, 3860}, {3853, 12100}, {3861, 10109}, {4301, 4669}, {4421, 34706}, {4677, 7982}, {5054, 38335}, {5055, 14269}, {5073, 15685}, {5076, 15693}, {5434, 34697}, {5562, 21969}, {5613, 25164}, {5617, 25154}, {5640, 16261}, {5656, 32064}, {5657, 9812}, {5890, 15305}, {5907, 21849}, {5913, 38951}, {5943, 46847}, {6033, 11632}, {6235, 6324}, {6248, 44422}, {6278, 22485}, {6281, 22484}, {6321, 8724}, {6785, 6787}, {7620, 9770}, {7710, 46034}, {7728, 20126}, {7775, 18546}, {7811, 34733}, {8597, 11676}, {9140, 10706}, {9144, 11005}, {9730, 16194}, {9760, 22575}, {9762, 22576}, {9766, 34505}, {9909, 34725}, {10127, 44804}, {10201, 18568}, {10707, 10711}, {10708, 10710}, {10709, 10716}, {10719, 10720}, {10723, 12117}, {10752, 13169}, {10753, 11161}, {11194, 34739}, {11235, 11236}, {11305, 41028}, {11306, 41029}, {11317, 13860}, {11455, 15072}, {11477, 15533}, {11812, 12102}, {12150, 34681}, {12355, 13188}, {14093, 35434}, {14163, 14214}, {14164, 14215}, {14892, 41987}, {15069, 15534}, {15679, 21669}, {15681, 15684}, {15686, 35404}, {15694, 35403}, {15718, 35401}, {16200, 37712}, {17578, 19708}, {18323, 44265}, {18377, 44278}, {18492, 30308}, {18552, 42853}, {18572, 44266}, {22491, 22492}, {23046, 38071}, {25175, 25223}, {25180, 25224}, {31145, 34631}, {31693, 41016}, {31694, 41017}, {31862, 31863}, {34621, 44442}, {36437, 36455}, {36490, 36730}, {36523, 38745}, {36551, 36729}, {36718, 36734}, {36719, 36733}, {36720, 36732}, {36721, 36731}, {36722, 36728}, {36723, 36726}, {36724, 36725}, {36990, 43273}, {38724, 38789}, {38732, 38743}, {41096, 41123}, {44262, 44288}, {44263, 44287}, {46977, 46985}, {46979, 46983}, {46980, 46988}, {46982, 46986}

  • X381 = reflection of Xi in Xj for these {i,j}: {2, 5}, {3, 2}, {4, 3845}, {5, 5066}, {6, 5476}, {20, 8703}, {21, 44257}, {22, 44262}, {23, 44266}, {24, 44270}, {25, 44275}, {26, 44278}, {52, 21849}, {140, 10109}, {165, 11231}, {186, 44282}, {376, 549}, {378, 44287}, {382, 3830}, {383, 44289}, {399, 5655}, {546, 3860}, {547, 11737}, {548, 11812}, {549, 547}, {550, 12100}, {568, 51}, {599, 11178}, {1113, 13626}, {1114, 13627}, {1116, 39494}, {1351, 20423}, {1482, 3656}, {1656, 19709}, {1657, 3534}, {1853, 23325}, {1995, 39487}, {2979, 15067}, {3095, 44422}, {3146, 33699}, {3167, 5654}, {3522, 15713}, {3524, 15699}, {3529, 19710}, {3534, 3}, {3543, 15687}, {3545, 38071}, {3576, 11230}, {3581, 32225}, {3627, 12101}, {3654, 10}, {3655, 551}, {3656, 946}, {3830, 4}, {3839, 23046}, {3843, 41099}, {3845, 546}, {3851, 41106}, {3860, 3856}, {3917, 10170}, {4930, 34647}, {5050, 14561}, {5054, 5055}, {5055, 3545}, {5066, 3850}, {5068, 41990}, {5073, 15682}, {5077, 37242}, {5085, 38317}, {5093, 14853}, {5094, 39484}, {5476, 19130}, {5587, 38140}, {5603, 38034}, {5655, 113}, {5657, 38042}, {5731, 38028}, {5790, 5587}, {5817, 38139}, {5858, 34508}, {5859, 34509}, {5886, 3817}, {5890, 5946}, {5946, 13364}, {6054, 22566}, {6055, 5461}, {6243, 21969}, {6321, 9880}, {7540, 428}, {7576, 13490}, {7610, 7617}, {7615, 20112}, {7618, 9771}, {7967, 10283}, {8182, 15597}, {8371, 39492}, {8598, 37459}, {8703, 140}, {8724, 114}, {9730, 5943}, {9766, 7775}, {9979, 44204}, {10031, 19907}, {10032, 19919}, {10109, 12811}, {10164, 10172}, {10165, 10171}, {10168, 25565}, {10246, 5886}, {10247, 5603}, {10295, 18579}, {10304, 11539}, {10606, 23329}, {10620, 20126}, {10992, 36521}, {11001, 550}, {11057, 34510}, {11159, 35930}, {11165, 11184}, {11178, 25561}, {11179, 597}, {11184, 8176}, {11362, 4745}, {11459, 15060}, {11632, 115}, {11812, 35018}, {11911, 11897}, {12100, 3628}, {12101, 3861}, {12103, 15759}, {12117, 33813}, {12188, 11632}, {12355, 6321}, {12702, 3654}, {13102, 25164}, {13103, 25154}, {13188, 8724}, {13340, 3917}, {14070, 10201}, {14093, 15694}, {14269, 3839}, {14643, 36518}, {14651, 38229}, {14666, 9172}, {14830, 6055}, {14848, 38072}, {14853, 38136}, {14855, 16836}, {14995, 14356}, {15041, 15061}, {15055, 34128}, {15061, 23515}, {15533, 34507}, {15534, 576}, {15561, 36519}, {15678, 31649}, {15681, 376}, {15682, 3627}, {15683, 15686}, {15684, 3543}, {15685, 20}, {15686, 34200}, {15687, 14893}, {15688, 5054}, {15689, 3524}, {15690, 3530}, {15691, 14891}, {15693, 1656}, {15694, 5071}, {15695, 631}, {15696, 15693}, {15697, 15712}, {15699, 14892}, {15700, 15703}, {15701, 3090}, {15704, 15690}, {15713, 12812}, {15716, 5070}, {15722, 7486}, {15759, 16239}, {15980, 37350}, {16194, 46847}, {16220, 10278}, {16836, 6688}, {17525, 16617}, {17538, 15711}, {17800, 11001}, {17813, 23048}, {18332, 5465}, {18405, 18376}, {18435, 15030}, {18493, 30308}, {18559, 38322}, {18575, 39486}, {19140, 25566}, {19706, 6918}, {19708, 632}, {19709, 3091}, {19710, 548}, {20126, 125}, {20128, 1651}, {20423, 5480}, {21151, 38171}, {21153, 38318}, {21154, 38319}, {21733, 11182}, {21849, 10110}, {21969, 5446}, {23039, 5891}, {25154, 5478}, {25164, 5479}, {25406, 38110}, {26446, 10175}, {27088, 10011}, {28460, 15670}, {30232, 14215}, {30233, 14214}, {31961, 31840}, {32447, 262}, {32519, 32447}, {32609, 14643}, {33699, 3853}, {33923, 11540}, {34153, 11694}, {34200, 10124}, {34473, 34127}, {34505, 18546}, {34682, 12150}, {34698, 5434}, {34707, 4421}, {34718, 3679}, {34726, 9909}, {34734, 7811}, {34740, 11194}, {34745, 3058}, {34748, 3241}, {34810, 14995}, {35434, 35403}, {35489, 16532}, {35752, 16001}, {35932, 44223}, {36330, 16002}, {36448, 42281}, {36466, 42280}, {36490, 36722}, {36521, 20399}, {36718, 36719}, {36720, 36490}, {36721, 36551}, {36723, 36724}, {36726, 36725}, {36729, 36727}, {36730, 36728}, {36731, 36729}, {36732, 36730}, {36734, 36733}, {37348, 3363}, {37477, 13857}, {37922, 37943}, {37956, 46451}, {38107, 38150}, {38224, 23514}, {38335, 14269}, {38693, 34126}, {38723, 38793}, {38724, 14644}, {38731, 38748}, {38732, 14639}, {38742, 38737}, {38754, 21154}, {38788, 38727}, {40280, 373}, {40727, 7615}, {41042, 22796}, {41043, 22797}, {41099, 3858}, {41106, 3857}, {41984, 41986}, {42278, 36466}, {42279, 36448}, {42733, 39491}, {42830, 18552}, {43273, 182}, {44202, 44564}, {44245, 44580}, {44255, 6675}, {44257, 46028}, {44261, 6676}, {44262, 46029}, {44265, 468}, {44266, 44961}, {44268, 16238}, {44270, 44235}, {44273, 6677}, {44275, 46030}, {44278, 13406}, {44280, 44452}, {44282, 46031}, {44284, 8728}, {44287, 39504}, {44750, 4846}, {44903, 15691}, {45700, 3829}, {46633, 46977}, {46634, 46983}

  • X381 = isogonal conjugate of X3431

  • X381 = isotomic conjugate of isogonal conjugate of X34417

  • X381 = complement of X376

  • X381 = anticomplement of X549

  • X381 = center of the orthocentroidal circle

  • X381 = centroid of the Euler triangle

  • X381 = center of equilateral triangle X4PU(5)

  • X381 = center of the Vu pedal-centroidal circle of X382

  • X381 = circumcircle-inverse of X7575

  • X381 = nine-point-circle-inverse of X11799

  • X381 = polar-circle-inverse of X10295

  • X381 = orthoptic-circle-of-Steiner-inellipse-inverse of X7426

  • X381 = orthoptic-circle-of-Steiner-circumellipse-inverse of X37901

  • X381 = Stammler-circle-inverse of X37924

  • X381 = Hutson-Parry-circle-inverse of X9169

  • X381 = circle-O(PU(5))-inverse of X4k

  • X381 = Kiepert-hyperbola-inverse of X6

  • X381 = crossdifference of every pair of points on line X526X647

  • X381 = polar conjugate of the isotomic conjugate of X37638

  • X381 = polar conjugate of the isogonal conjugate of X5158

  • X381 = Thomson isogonal conjugate of X7712

  • X381 = orthic isogonal conjugate of X40909

  • X381 = psi-transform of X9140

  • X381 = X14483-anticomplementary conjugate of X8

  • X381 = Xi-complementary conjugate of Xj for these (i,j): {3426, 10}, {9064, 8062}, {36889, 2887}

  • X381 = Xi-Ceva conjugate of Xj for these (i,j): {4, 40909}, {1302, 523}, {4993, 5158}, {7578, 6}, {44135, 37638}, {46808, 18487}

  • X381 = Xi-cross conjugate of Xj for these (i,j): {5158, 37638}, {18487, 46808}

  • X381 = Xi-isoconjugate of Xj for these (i,j): {1, 3431}, {48, 43530}, {255, 16263}, {2159, 46809}, {6149, 18316}

  • X381 = cevapoint of X5158 and X34417

  • X381 = crosspoint of Xi and Xj for these (i,j): {2, 36889}, {264, 34289}

  • X381 = crosssum of Xi and Xj for these (i,j): {6, 26864}, {184, 5063}, {1511, 10564}

  • X381 = trilinear pole of line {18487, 32225}

  • X381 = crossdifference of every pair of points on line {526, 647}

  • X381 = X8-beth conjugate of X3654

  • X381 = X2-daleth conjugate of X44216

  • X381 = X1-zayin conjugate of X3431

  • X381 = pole of the line X2X6 wrt the circle {X2,X13,X14,X111,X476}}

  • X381 = pole of the Napoleon axis wrt the Lester circle

  • X381 = X3-of-4th-Brocard-triangle

  • X381 = X3-of-orthocentroidal-triangle

  • X381 = center of conic that is the locus of orthopoles of lines passing through X2

  • X381 = harmonic center of circumcircle and nine-point circle

  • X381 = centroid of antipedal triangle of X2 wrt medial triangle

  • X381 = homothetic center of orthic triangle and 2nd isogonal triangle of X4; see X36

  • X381 = pole of line X2X6 wrt Hutson-Parry circle

  • X381 = Artzt-to-McCay similarity image of X98

  • X381 = intersection of Fermat axes of ABC and Artzt triangle

  • X381 = centroid of maltitude quadrangle of quadrangle ABCX2

  • X381 = homothetic center of X5-altimedial and X4-anti-altimedial triangles

  • X381 = X3576-of-orthic-triangle if ABC is acute

  • X381 = trisector nearest X5 of segment X4X5

  • X381 = {X3,X4}-harmonic conjugate of X382

  • X381 = {X2043,X2044}-harmonic conjugate of X5

  • X381 = homothetic center of ABC and Ehrmann mid-triangle

  • X381 = homothetic center of Ehrmann vertex-triangle and tangential triangle

  • X381 = homothetic center of Ehrmann side-triangle and orthic triangle

  • X381 = Johnson-to-Ehrmann-mid similarity image of X2

  • X381 = barycentric product Xi*Xj for these {i,j}: {4, 37638}, {5, 4993}, {6, 44135}, {30, 46808}, {76, 34417}, {92, 18477}, {94, 3581}, {264, 5158}, {671, 32225}, {1494, 18487}, {1502, 34416}, {1531, 16080}, {2349, 18486}, {2996, 21970}, {4550, 34289}, {14165, 18478}, {14314, 46456}

  • X381 = barycentric quotient Xi/Xj for these {i,j}: {4, 43530}, {6, 3431}, {30, 46809}, {393, 16263}, {1531, 11064}, {1989, 18316}, {3581, 323}, {4550, 15066}, {4993, 95}, {5158, 3}, {8749, 22455}, {14314, 8552}, {14533, 46091}, {15362, 44555}, {18477, 63}, {18485, 18487}, {18486, 14206}, {18487, 30}, {21970, 193}, {32225, 524}, {34416, 32}, {34417, 6}, {37638, 69}, {40909, 37645}, {44135, 76}, {46808, 1494}

  • X381 = {Xi,Xj}-harmonic conjugate of Xk for these (i,j,k): {1, 9955, 18493}, {1, 10895, 9654}, {1, 10896, 9669}, {1, 18480, 18525}, {1, 18492, 18480}, {1, 18525, 18526}, {1, 18527, 18530}, {1, 18529, 18528}, {1, 18542, 18545}, {1, 18544, 18543}, {1, 30308, 38021}, {1, 45630, 18544}, {1, 45631, 18542}, {2, 3, 5054}, {2, 5, 5055}, {2, 20, 3524}, {2, 376, 549}, {2, 382, 15688}, {2, 384, 33220}, {2, 428, 9909}, {2, 452, 17561}, {2, 546, 14269}, {2, 547, 15703}, {2, 549, 15694}, {2, 550, 15707}, {2, 631, 11539}, {2, 858, 32216}, {2, 1003, 11288}, {2, 1370, 43957}, {2, 1513, 40248}, {2, 1657, 15706}, {2, 3090, 15699}, {2, 3091, 3545}, {2, 3146, 10304}, {2, 3522, 15708}, {2, 3523, 15709}, {2, 3524, 140}, {2, 3529, 17504}, {2, 3534, 15693}, {2, 3543, 376}, {2, 3545, 5}, {2, 3627, 15689}, {2, 3830, 3534}, {2, 3832, 3839}, {2, 3839, 4}, {2, 3843, 38335}, {2, 3845, 3830}, {2, 3855, 38071}, {2, 5025, 33219}, {2, 5054, 3526}, {2, 5055, 1656}, {2, 5059, 15705}, {2, 5064, 34609}, {2, 5066, 19709}, {2, 5071, 547}, {2, 6175, 44217}, {2, 6756, 10245}, {2, 7576, 14070}, {2, 7714, 10154}, {2, 7841, 11287}, {2, 8352, 5077}, {2, 8370, 11286}, {2, 8597, 35955}, {2, 8703, 15701}, {2, 10304, 631}, {2, 11001, 12100}, {2, 11112, 16417}, {2, 11113, 16418}, {2, 11114, 16370}, {2, 11286, 33237}, {2, 11299, 11301}, {2, 11300, 11302}, {2, 11303, 11298}, {2, 11304, 11297}, {2, 11317, 11159}, {2, 11318, 33240}, {2, 11361, 1003}, {2, 11539, 46219}, {2, 12101, 15685}, {2, 14002, 37907}, {2, 14033, 8369}, {2, 14035, 33255}, {2, 14036, 8366}, {2, 14039, 8368}, {2, 14041, 7841}, {2, 14063, 33251}, {2, 14068, 33187}, {2, 14269, 382}, {2, 14893, 15684}, {2, 15640, 19708}, {2, 15681, 15700}, {2, 15682, 8703}, {2, 15683, 15692}, {2, 15684, 14093}, {2, 15685, 15716}, {2, 15686, 15718}, {2, 15687, 15681}, {2, 15688, 15720}, {2, 15690, 15722}, {2, 15692, 15702}, {2, 15694, 15723}, {2, 15697, 15719}, {2, 15698, 15713}, {2, 15699, 5070}, {2, 15702, 10124}, {2, 15705, 10303}, {2, 15708, 3525}, {2, 15709, 632}, {2, 15710, 14869}, {2, 16041, 33184}, {2, 16865, 15671}, {2, 17532, 17528}, {2, 17538, 41983}, {2, 17561, 6675}, {2, 17577, 17532}, {2, 17579, 16371}, {2, 17677, 11359}, {2, 18559, 18324}, {2, 18566, 18561}, {2, 18568, 18564}, {2, 19686, 33246}, {2, 19708, 11812}, {2, 23046, 3843}, {2, 24608, 1375}, {2, 26122, 25518}, {2, 26255, 468}, {2, 26786, 27055}, {2, 26833, 26994}, {2, 30775, 5159}, {2, 30922, 46531}, {2, 30976, 37370}, {2, 31048, 857}, {2, 31105, 858}, {2, 31133, 31152}, {2, 31156, 15670}, {2, 31789, 28451}, {2, 32986, 8359}, {2, 32996, 33278}, {2, 33006, 33228}, {2, 33007, 35297}, {2, 33013, 44543}, {2, 33016, 8370}, {2, 33017, 8356}, {2, 33187, 16925}, {2, 33192, 33008}, {2, 33219, 7866}, {2, 33220, 32954}, {2, 33228, 11318}, {2, 33251, 6656}, {2, 33255, 7807}, {2, 33264, 33273}, {2, 33265, 33274}, {2, 33272, 33215}, {2, 33278, 7791}, {2, 33285, 8360}, {2, 33699, 15695}, {2, 33703, 45759}, {2, 34938, 43934}, {2, 35927, 33216}, {2, 36436, 36457}, {2, 36439, 36456}, {2, 36445, 18585}, {2, 36454, 36439}, {2, 36457, 36438}, {2, 36463, 15765}, {2, 37038, 19279}, {2, 37077, 378}, {2, 37150, 19277}, {2, 37170, 37352}, {2, 37171, 37351}, {2, 37375, 17556}, {2, 38071, 3851}, {2, 38320, 3515}, {2, 38322, 37922}, {2, 38335, 1657}, {2, 41099, 3845}, {2, 41106, 5066}, {2, 43957, 16419}, {2, 44442, 10691}, {2, 44462, 46825}, {2, 44466, 46824}, {2, 44579, 11331}, {2, 46333, 15712}, {2, 46451, 7552}, {2, 46856, 36186}, {2, 46857, 36185}, {2, 46868, 44889}, {2, 46869, 44891}, {3, 4, 382}, {3, 5, 1656}, {3, 25, 2070}, {3, 376, 14093}, {3, 382, 1657}, {3, 547, 15723}, {3, 549, 15700}, {3, 1598, 7517}, {3, 1656, 3526}, {3, 1657, 15696}, {3, 2072, 30771}, {3, 3091, 5072}, {3, 3516, 35498}, {3, 3520, 35496}, {3, 3524, 15716}, {3, 3526, 15720}, {3, 3534, 15688}, {3, 3843, 4}, {3, 3845, 38335}, {3, 3851, 5}, {3, 5054, 15693}, {3, 5055, 2}, {3, 5070, 140}, {3, 5072, 5079}, {3, 5073, 20}, {3, 5899, 22}, {3, 6642, 43809}, {3, 6913, 7489}, {3, 6918, 45976}, {3, 7387, 13564}, {3, 7506, 45735}, {3, 7517, 2937}, {3, 7529, 7506}, {3, 7540, 34726}, {3, 7579, 5094}, {3, 13621, 24}, {3, 14269, 3830}, {3, 14893, 35434}, {3, 15681, 376}, {3, 15684, 15681}, {3, 15685, 15689}, {3, 15689, 8703}, {3, 15693, 15706}, {3, 15694, 549}, {3, 15695, 10304}, {3, 15701, 3524}, {3, 15703, 15694}, {3, 15707, 12100}, {3, 15718, 15692}, {3, 16418, 28443}, {3, 17800, 550}, {3, 18378, 26}, {3, 18531, 18536}, {3, 18534, 12083}, {3, 18535, 18534}, {3, 19709, 5055}, {3, 28453, 16370}, {3, 35400, 15686}, {3, 35401, 35400}, {3, 35403, 15684}, {3, 37234, 13743}, {3, 37411, 16117}, {3, 37922, 18324}, {3, 44457, 35243}, {3, 46219, 631}, {4, 5, 3}, {4, 20, 3627}, {4, 24, 12173}, {4, 25, 18494}, {4, 140, 5073}, {4, 186, 35480}, {4, 235, 1598}, {4, 376, 3543}, {4, 378, 44438}, {4, 382, 5076}, {4, 403, 25}, {4, 427, 1597}, {4, 442, 37411}, {4, 546, 3843}, {4, 547, 15681}, {4, 549, 15684}, {4, 631, 3146}, {4, 1346, 1344}, {4, 1347, 1345}, {4, 1532, 19541}, {4, 1594, 1593}, {4, 1596, 18535}, {4, 1656, 1657}, {4, 2043, 18587}, {4, 2044, 18586}, {4, 2476, 6985}, {4, 3088, 13488}, {4, 3089, 6756}, {4, 3090, 20}, {4, 3091, 5}, {4, 3146, 3853}, {4, 3153, 44288}, {4, 3520, 35490}, {4, 3524, 15682}, {4, 3525, 33703}, {4, 3529, 17578}, {4, 3541, 1885}, {4, 3542, 3575}, {4, 3543, 15687}, {4, 3544, 631}, {4, 3545, 2}, {4, 3547, 7553}, {4, 3628, 17800}, {4, 3830, 38335}, {4, 3832, 546}, {4, 3839, 3845}, {4, 3845, 14269}, {4, 3850, 3851}, {4, 3851, 1656}, {4, 3854, 3850}, {4, 3855, 3091}, {4, 5055, 3534}, {4, 5056, 550}, {4, 5066, 5055}, {4, 5067, 3529}, {4, 5068, 140}, {4, 5071, 376}, {4, 5072, 3526}, {4, 5079, 15696}, {4, 5084, 6851}, {4, 5133, 9818}, {4, 5169, 31861}, {4, 5187, 37356}, {4, 6622, 7487}, {4, 6623, 1596}, {4, 6804, 34938}, {4, 6816, 14790}, {4, 6824, 7491}, {4, 6826, 6923}, {4, 6828, 3560}, {4, 6829, 7580}, {4, 6830, 1012}, {4, 6834, 37468}, {4, 6835, 6917}, {4, 6837, 37290}, {4, 6841, 37234}, {4, 6843, 6907}, {4, 6844, 8727}, {4, 6846, 31789}, {4, 6848, 20420}, {4, 6849, 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37835}, {16645, 42155, 16}, {16772, 42164, 42150}, {16773, 42165, 42151}, {16808, 16809, 6}, {16808, 42125, 42815}, {16808, 42128, 42962}, {16809, 42125, 42963}, {16809, 42128, 42816}, {16853, 44284, 5054}, {16868, 18559, 37943}, {16868, 18566, 37922}, {16898, 33283, 8363}, {16922, 33256, 33004}, {16923, 19696, 33014}, {16924, 33251, 2}, {16925, 32963, 33249}, {16962, 16964, 41101}, {16962, 41101, 22236}, {16963, 16965, 41100}, {16963, 41100, 22238}, {16966, 19107, 11480}, {16966, 36967, 16241}, {16966, 43227, 19107}, {16967, 19106, 11481}, {16967, 36968, 16242}, {16967, 43226, 19106}, {17504, 19708, 3}, {17504, 19710, 548}, {17504, 35018, 2}, {17504, 45761, 15692}, {17532, 17556, 2}, {17532, 44217, 6175}, {17538, 46936, 14869}, {17549, 28461, 6914}, {17556, 17577, 17528}, {17566, 37256, 19537}, {17567, 37435, 17563}, {17577, 37375, 2}, {17578, 35018, 3}, {17685, 33045, 33036}, {17800, 46219, 3}, {17928, 35502, 12084}, {18281, 23410, 6642}, {18281, 38323, 3}, {18324, 18561, 3534}, {18325, 32216, 3534}, {18350, 37472, 1147}, {18357, 22791, 8}, {18358, 21850, 69}, {18369, 45735, 7506}, {18377, 18378, 382}, {18377, 44958, 18378}, {18388, 18390, 6}, {18388, 18474, 18445}, {18390, 18418, 113}, {18390, 18474, 265}, {18391, 39542, 1159}, {18403, 46030, 7545}, {18424, 43457, 6}, {18439, 37481, 185}, {18440, 45375, 26346}, {18440, 45376, 26336}, {18445, 18451, 399}, {18451, 18474, 18440}, {18480, 18493, 18526}, {18483, 38076, 3654}, {18488, 43817, 20299}, {18493, 18525, 1}, {18504, 43865, 9704}, {18509, 18511, 3818}, {18509, 19130, 18512}, {18510, 18512, 6}, {18510, 26336, 39899}, {18511, 19130, 18510}, {18512, 26346, 39899}, {18527, 18529, 18525}, {18528, 18530, 18526}, {18531, 18535, 382}, {18531, 31723, 7574}, {18534, 18536, 1657}, {18534, 31723, 382}, {18535, 18537, 18536}, {18536, 37347, 3526}, {18538, 23259, 6199}, {18538, 42215, 3068}, {18542, 18544, 18525}, {18543, 18545, 18526}, {18559, 18566, 3830}, {18559, 37943, 24}, {18560, 37119, 3516}, {18565, 37119, 35498}, {18566, 37922, 382}, {18566, 44270, 18559}, {18568, 44275, 7576}, {18572, 44961, 23}, {18581, 42106, 5318}, {18582, 42103, 5321}, {18583, 39884, 6776}, {18584, 31489, 7603}, {18584, 44526, 31489}, {18585, 36439, 36455}, {18585, 42281, 2044}, {18586, 18587, 3}, {18762, 23249, 6395}, {18762, 42216, 3069}, {18907, 43291, 7735}, {19130, 22796, 14}, {19130, 22797, 13}, {19130, 45438, 13785}, {19130, 45439, 13665}, {19546, 37331, 19550}, {19550, 37331, 3}, {19686, 33246, 1003}, {19687, 33249, 16925}, {19697, 33186, 14069}, {19709, 35403, 15694}, {19709, 38335, 3526}, {19710, 35018, 15709}, {20030, 27868, 28237}, {20192, 45303, 44569}, {20299, 22802, 64}, {20423, 22491, 20426}, {20423, 22492, 20425}, {20425, 20426, 1351}, {20957, 25641, 38580}, {21308, 39504, 1656}, {21475, 21476, 11340}, {21735, 41984, 15701}, {21735, 44682, 3}, {21735, 46935, 140}, {21869, 21898, 33062}, {22493, 22494, 15533}, {22495, 22496, 15534}, {22605, 22606, 6290}, {22615, 42582, 6449}, {22634, 22635, 6289}, {22644, 42583, 6450}, {22753, 22758, 22765}, {22796, 22797, 3818}, {22804, 43865, 18379}, {22833, 22955, 22979}, {23046, 41106, 3}, {23046, 41990, 3627}, {23251, 42262, 372}, {23261, 42265, 371}, {23302, 42085, 42116}, {23302, 42101, 42085}, {23302, 42940, 42942}, {23302, 43104, 42911}, {23303, 42086, 42115}, {23303, 42102, 42086}, {23303, 42941, 42943}, {23303, 43101, 42910}, {23323, 46030, 4}, {24828, 24833, 24844}, {26326, 26386, 45369}, {26327, 26410, 45370}, {26328, 26466, 45610}, {26329, 26467, 45609}, {26332, 26470, 10680}, {26333, 37820, 10738}, {26336, 26346, 18440}, {27124, 27177, 2}, {27406, 27536, 33305}, {28033, 28103, 33302}, {28067, 28140, 33306}, {28263, 28382, 859}, {28431, 28721, 441}, {28447, 28448, 37955}, {29413, 29465, 46497}, {29521, 29727, 46575}, {29565, 29780, 46574}, {29998, 30070, 46514}, {30308, 38021, 9955}, {30771, 31726, 1657}, {30775, 40132, 2}, {31133, 31152, 34609}, {31133, 31180, 31181}, {31140, 31141, 3679}, {31159, 31160, 3679}, {31236, 35480, 18570}, {31489, 44526, 574}, {31664, 40894, 3}, {31665, 40895, 3}, {31693, 31694, 2}, {31693, 37351, 37352}, {31693, 37352, 37170}, {31694, 37351, 37171}, {31694, 37352, 37351}, {31723, 37347, 3}, {31824, 32156, 34792}, {31841, 40100, 38584}, {31861, 44263, 44438}, {32006, 32828, 7767}, {32369, 32379, 32402}, {32460, 46859, 2}, {32461, 46858, 2}, {32488, 33269, 7388}, {32489, 33269, 7389}, {32785, 42225, 6445}, {32786, 42226, 6446}, {32789, 42275, 6451}, {32790, 42276, 6452}, {32951, 33198, 33185}, {32961, 33255, 2}, {32962, 32996, 7791}, {32962, 33278, 2}, {32963, 33187, 2}, {32964, 33280, 33250}, {32965, 33279, 19695}, {32966, 33018, 384}, {32968, 32974, 8362}, {32971, 32980, 14064}, {32972, 32979, 14001}, {32974, 32991, 32968}, {32975, 33238, 32990}, {32976, 33239, 32989}, {32981, 32988, 32970}, {32982, 32987, 16043}, {32992, 33229, 7791}, {32994, 33264, 2}, {32997, 33009, 33001}, {32998, 33280, 32964}, {32999, 33279, 32965}, {33002, 33019, 7824}, {33004, 33010, 16922}, {33005, 33017, 2}, {33006, 33016, 2}, {33008, 33192, 8353}, {33016, 33228, 11286}, {33028, 33057, 33034}, {33029, 33056, 33033}, {33030, 33046, 33035}, {33184, 37350, 16041}, {33215, 33272, 8354}, {33216, 35927, 27088}, {33237, 33240, 2}, {33244, 33270, 33000}, {33264, 33273, 35955}, {33332, 44279, 35502}, {33532, 40916, 3}, {33923, 35417, 14893}, {33923, 41983, 15711}, {34200, 35404, 15683}, {34417, 37638, 21970}, {34484, 35500, 7488}, {34551, 34552, 3530}, {34559, 34562, 3850}, {35255, 42225, 9541}, {35382, 35400, 3526}, {35400, 35401, 3543}, {35401, 35404, 35434}, {35403, 35434, 5076}, {35404, 35408, 3146}, {35481, 37118, 11410}, {35481, 44452, 3}, {35493, 37968, 3}, {35500, 37440, 3}, {35732, 42282, 3525}, {35738, 42282, 3}, {35800, 35803, 3297}, {35801, 35802, 3298}, {35822, 35823, 6}, {35948, 35949, 8598}, {36169, 36184, 36193}, {36436, 36439, 36438}, {36436, 36454, 2}, {36436, 36455, 18587}, {36437, 36454, 18586}, {36437, 36457, 3}, {36438, 36456, 2}, {36439, 36455, 3}, {36439, 36457, 2}, {36445, 36463, 3839}, {36445, 41106, 2043}, {36448, 36466, 19709}, {36452, 36470, 16645}, {36453, 36469, 16644}, {36454, 36457, 36456}, {36463, 41106, 2044}, {36490, 36728, 36732}, {36526, 36530, 36527}, {36526, 36654, 3}, {36530, 36716, 3}, {36551, 36727, 36731}, {36557, 36561, 36558}, {36652, 36661, 3}, {36652, 36687, 5}, {36660, 36673, 5}, {36661, 36686, 4}, {36683, 36694, 5}, {36686, 36687, 3}, {36709, 37342, 3}, {36714, 37343, 3}, {36722, 36730, 36720}, {36969, 37835, 16}, {36969, 42155, 42127}, {36969, 42918, 37835}, {36970, 37832, 15}, {36970, 42154, 42126}, {36970, 42919, 37832}, {37077, 44263, 3830}, {37144, 37145, 2049}, {37162, 37433, 6903}, {37170, 37171, 2}, {37172, 37173, 439}, {37196, 37453, 186}, {37230, 37234, 382}, {37332, 37333, 3}, {37340, 37341, 14001}, {37349, 37353, 22}, {37351, 37352, 2}, {37353, 44262, 5055}, {37439, 43957, 2}, {37458, 37942, 6353}, {37460, 38282, 37935}, {37517, 43150, 40341}, {37638, 40909, 3581}, {37640, 42142, 43403}, {37640, 43403, 11542}, {37641, 42139, 43404}, {37641, 43404, 11543}, {37984, 44920, 15760}, {38071, 41099, 3}, {38071, 41991, 3860}, {38072, 41042, 42975}, {38072, 41043, 42974}, {38141, 38142, 38034}, {39504, 44263, 378}, {39530, 44924, 30258}, {39565, 39590, 32}, {40250, 40277, 3845}, {40647, 46849, 11381}, {40693, 42159, 398}, {40693, 42921, 42166}, {40694, 42162, 397}, {40694, 42920, 42163}, {41016, 41017, 4}, {41099, 41106, 2}, {41099, 41990, 15685}, {41107, 42813, 42973}, {41107, 42973, 5340}, {41108, 42814, 42972}, {41108, 42972, 5339}, {41112, 41120, 43229}, {41113, 41119, 43228}, {41121, 42972, 61}, {41122, 42973, 62}, {41748, 41750, 15534}, {41984, 44245, 44580}, {41984, 44580, 140}, {41987, 41990, 3090}, {41989, 44904, 5}, {41990, 44903, 11737}, {41990, 45762, 5071}, {42085, 42114, 23302}, {42086, 42111, 23303}, {42089, 42105, 42088}, {42092, 42104, 42087}, {42093, 42098, 15}, {42093, 42154, 36970}, {42093, 42919, 42132}, {42094, 42095, 16}, {42094, 42155, 36969}, {42094, 42918, 42129}, {42095, 42155, 16645}, {42096, 43029, 10645}, {42097, 43028, 10646}, {42098, 42154, 16644}, {42101, 42114, 42116}, {42101, 42942, 42940}, {42101, 43104, 42942}, {42102, 42111, 42115}, {42102, 42943, 42941}, {42102, 43101, 42943}, {42103, 42110, 11485}, {42106, 42107, 11486}, {42111, 42115, 42951}, {42111, 42910, 43101}, {42114, 42116, 42950}, {42114, 42911, 43104}, {42117, 42146, 11488}, {42118, 42143, 11489}, {42121, 42137, 42120}, {42124, 42136, 42119}, {42125, 42128, 6}, {42125, 42974, 42975}, {42125, 42975, 14}, {42126, 42132, 15}, {42127, 42129, 16}, {42128, 42974, 13}, {42128, 42975, 42974}, {42147, 42598, 42152}, {42148, 42599, 42149}, {42149, 42161, 42148}, {42152, 42160, 42147}, {42159, 42921, 40693}, {42162, 42920, 40694}, {42258, 42582, 5418}, {42259, 42583, 5420}, {42268, 42273, 3311}, {42269, 42270, 3312}, {42274, 42284, 6398}, {42277, 42283, 6221}, {42278, 42279, 1656}, {42280, 42281, 3091}, {42431, 42489, 5237}, {42432, 42488, 5238}, {42474, 42626, 43029}, {42475, 42625, 43028}, {42568, 43339, 6484}, {42569, 43338, 6485}, {42789, 42790, 35473}, {42791, 43107, 42945}, {42792, 43100, 42944}, {42807, 42808, 3850}, {42815, 42816, 6}, {42815, 42962, 42128}, {42815, 42963, 42816}, {42816, 42962, 42815}, {42816, 42963, 42125}, {42830, 42853, 42831}, {42894, 42895, 6}, {42894, 43030, 43031}, {42895, 43031, 43030}, {42910, 42941, 42115}, {42911, 42940, 42116}, {42936, 43632, 5352}, {42937, 43633, 5351}, {42940, 42942, 42085}, {42941, 42943, 42086}, {42942, 43104, 23302}, {42943, 43101, 23303}, {42962, 42963, 6}, {42974, 42975, 6}, {43030, 43031, 6}, {43193, 43239, 5237}, {43194, 43238, 5238}, {43209, 43255, 6456}, {43210, 43254, 6455}, {43211, 43257, 6407}, {43212, 43256, 6408}, {43821, 43831, 43845}, {43893, 46450, 37949}, {43957, 44454, 3534}, {44211, 44218, 549}, {44212, 44218, 44214}, {44236, 44452, 37118}, {44245, 44682, 21735}, {44276, 44440, 18325}, {44288, 46029, 22}, {44441, 44804, 1597}, {44580, 44682, 3524}, {45375, 45376, 18440}, {45438, 45439, 3818}, {45544, 45554, 45578}, {45545, 45555, 45579}, {45630, 45631, 18480}, {45924, 45926, 45923}, {46470, 46471, 378}

Notes

As a point on the Euler line, X381 has Shinagawa coefficients \((1,3)\).

Let A' be the reflection of X3 in A, and define B’and C' cyclically. Let A″ be the reflection of X3 in BC, and define B″ and C″ cyclically. The lines A'A″, B'B″, C'C″ concur in X381.

Let Pa be the parabola with focus A and directrix BC. Let La be the polar of X3 wrt Pa. Define Lb and Lc cyclically. Let A' = Lb∩Lc, B' = Lc∩La, C' = La∩Lb. The symmedian point of triangle A'B'C' is X381. Analogously, let La be the trilinear polar of A wrt BCX3, and define Lb and Lc cyclically. Let A'=Lb∩Lc, B'=Lc∩La, C'=La∩Lb. Equivalently, A'B'C' is the cevian triangle of X3 wrt the cevian triangle of X3. Also, let A″ be the reflection of A' in BC, and define B″ and C″ cyclically. The lines AA″, BB″, CC″ concur in X381. Finally, let A' be the orthocenter of BCX6, and define B' and C' cyclically; then X381 is the centroid of A'B'C'. (Randy Hutson, September 5, 2015)

Let Sa be the similitude center of the orthocentroidal triangle and the A-altimedial triangle. Define Sb and Sc cyclically. The lines ASa, BSb, CSc concur in X381. (Randy Hutson, December 10, 2016)

Let A1B1C1 and A2B2C2 be the 1st and 2nd Ehrmann circumscribing triangles. Let A' be the crosspoint of A1 and A2, and define B', C' cyclically. The lines AA', BB', CC' concur in X381. (Randy Hutson, June 27, 2018)