X387

INTERSECTION OF LINES X(1,2) AND X(4,6)

X387 = crossdifference of every pair of points on line X520X649
< 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) { 1, 2 }: Nagel Line { 4, 6 }: Van Aubel Line { 20, 58 }: Central Line L(20, 58) { 65, 278 }: Central Line L(65, 278) { 81, 377 }: Central Line L(81, 377) { 40, 579 }: Central Line L(40, 579) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) 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_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_377 = EULER LINE INTERCEPT OF LINE X(7)X(8) (0.5473, 0.2258) X_40 = BEVAN POINT (0.4286, -0.0292) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_387 = INTERSECTION OF LINES X(1,2) AND X(4,6) (0.5994, 0.2607) A B C X1 X2 X4 X6 X20 X58 X65 X278 X81 X377 X40 X579 X387 (a, b, c) = (5, 6, 7) | AB = 1

X387 (INTERSECTION OF LINES X(1,2) AND X(4,6)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc[-a^{4} + 2a^{2}(a + b + c)^{2} + (b^{2} - c^{2})^{2}]\)
Barycentrics: \(-a^{4} + 2a^{2}(a + b + c)^{2} + (b^{2} - c^{2})^{2}\)
Search Value (6, 9, 13): \(1.128882560427\)
▸ Incident Central Lines107 lines

{1, 2}, {4, 6}, {7, 23537}, {20, 58}, {31, 4294}, {40, 579}, {46, 3101}, {55, 1612}, {57, 5930}, {65, 278}, {69, 16062}, {81, 377}, {193, 1330}, {219, 2551}, {230, 7410}, {333, 13725}, {341, 18147}, {346, 2901}, {376, 4252}, {390, 595}, {442, 5712}, {443, 940}, {452, 1724}, {497, 16466}, {580, 6987}, {581, 6908}, {631, 4255}, {942, 4000}, {950, 1453}, {966, 4205}, {990, 9799}, {999, 16415}, {1058, 1191}, {1104, 3488}, {1108, 4261}, {1126, 5261}, {1203, 1479}, {1214, 1788}, {1448, 18623}, {1449, 5717}, {1468, 4293}, {1617, 16453}, {1723, 12514}, {1743, 12572}, {1780, 6872}, {1838, 3914}, {1992, 17677}, {2047, 3068}, {2082, 7713}, {2271, 6998}, {2334, 15888}, {2345, 5295}, {2478, 16471}, {2550, 5711}, {3089, 3192}, {3189, 5266}, {3295, 16290}, {3339, 3668}, {3419, 5716}, {3487, 3772}, {3522, 4257}, {3523, 4256}, {3618, 13740}, {3695, 17314}, {3751, 13161}, {3767, 20970}, {3868, 4463}, {3874, 4310}, {3927, 4419}, {3945, 4208}, {4219, 8885}, {4251, 5304}, {4259, 18178}, {4260, 10441}, {4267, 19262}, {4356, 18249}, {4383, 5084}, {4648, 8728}, {4653, 17558}, {5021, 7738}, {5051, 5739}, {5082, 5710}, {5165, 6361}, {5264, 17784}, {5324, 13730}, {5396, 6825}, {5398, 6868}, {5587, 5747}, {5707, 6826}, {5713, 6843}, {5718, 6856}, {5814, 5839}, {6392, 17499}, {6857, 19765}, {7380, 7736}, {7682, 8282}, {7742, 16451}, {8676, 17922}, {9708, 16848}, {10480, 10822}, {10590, 21935}, {11109, 11427}, {11433, 17555}, {16704, 17676}, {17054, 17366}, {17685, 20158}, {19543, 22770}

▸ Functional Relations1 relation

  • X387 = crossdifference of every pair of points on line X520X649