X3641

2nd KIRIKAMI POINT

X3641 = X1-of-inner-Grebe-triangle
< 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, 6 }: Incenter–Symmedian Line { 8, 176 }: Central Line L(8, 176) { 517, 1161 }: Central Line L(517, 1161) { 482, 2550 }: Central Line L(482, 2550) { 3083, 3681 }: Central Line L(3083, 3681) { 3084, 3873 }: Central Line L(3084, 3873) 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_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_8 = NAGEL POINT (0.4694, 0.1333) X_176 = EQUAL DETOUR POINT (0.5803, 0.2537) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1161 = CIRCUMCENTER OF INNER GREBE TRIANGLE (0.8742, 0.7201) X_482 = 2nd EPPSTEIN POINT (0.5835, 0.2611) X_2550 = INSIMILICENTER(SPIEKER CIRCLE, (X(4),2R)) (0.5298, 0.2051) X_3083 = INTERSECTION OF LINES X(1)X(2) AND X(37)X(494) (0.5529, 0.2152) X_3681 = com(EXTOUCH TRIANGLE) (0.4476, 0.0933) X_3084 = INTERSECTION OF LINES X(1)X(2) AND X(37)X(493) (0.3591, 0.0252) X_3873 = com[INVERSE(n(3rd EULER TRIANGLE))] (0.6272, 0.3066) X_3641 = 2nd KIRIKAMI POINT (0.6784, 0.3603) A B C X1 X6 X8 X176 X517 X1161 X482 X2550 X3083 X3681 X3084 X3873 X3641 (a, b, c) = (5, 6, 7) | AB = 1

X3641 (2nd KIRIKAMI POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a (b^{2} + c^{2} - a (b + c) - S) : :\)
Search Value (6, 9, 13): \(-2.523977204829\)
▸ Linear Combinations1 combination

  • X3641 = \(3\) X1 - \(2\) X45713, \(3\) X3576 - \(4\) X45716, \(3\) X3640 - \(4\) X45713, X3640 - \(4\) X45714, \(3\) X5861 - X12627, X45713 - \(3\) X45714

▸ Incident Central Lines71 lines

{1, 6}, {3, 11497}, {8, 176}, {10, 5591}, {30, 16130}, {40, 11824}, {55, 8198}, {65, 10975}, {142, 30341}, {144, 30333}, {145, 30334}, {200, 13389}, {355, 6215}, {482, 2550}, {515, 5871}, {517, 1161}, {519, 5861}, {537, 24831}, {730, 6273}, {944, 10783}, {946, 6202}, {952, 5875}, {976, 36566}, {982, 8941}, {1373, 5880}, {1385, 26341}, {1482, 11916}, {1659, 4847}, {1702, 8396}, {1829, 11388}, {1837, 10925}, {2362, 39959}, {2800, 12753}, {2802, 13269}, {2809, 6212}, {3057, 10927}, {3083, 3681}, {3084, 3873}, {3244, 26339}, {3576, 45552}, {3579, 35246}, {5252, 10923}, {5393, 24477}, {5405, 25568}, {5587, 10514}, {5595, 9798}, {5657, 10517}, {5688, 10513}, {5698, 31568}, {5881, 6281}, {6001, 6258}, {6204, 30319}, {8216, 12440}, {8217, 12441}, {8974, 8983}, {9615, 45531}, {9941, 9994}, {10792, 12194}, {11901, 12438}, {12698, 40268}, {13949, 13971}, {18480, 18509}, {18525, 26336}, {26334, 45711}, {26335, 45712}, {26337, 45718}, {35641, 35792}, {35642, 35795}, {36480, 36535}, {45550, 45715}, {45594, 45717}

▸ Functional Relations3 relations

  • X3641 = reflection of Xi in Xj for these {i,j}: {1, 45714}, {3640, 1}, {12697, 1161}, {45719, 3244}

  • X3641 = X1-of-inner-Grebe-triangle

  • X3641 = {Xi,Xj}-harmonic conjugate of Xk for these (i,j,k): {1, 6, 11370}, {1, 3751, 18992}, {1, 5223, 30556}, {1, 5588, 7968}, {1, 5589, 6}, {1, 18991, 11371}, {1, 19003, 45399}, {1, 19004, 1386}, {1, 45427, 18991}, {6, 5605, 1}, {6, 10929, 10040}, {6, 10931, 10048}, {8, 1271, 5689}, {3242, 7969, 1}, {4663, 45399, 19003}, {5589, 5605, 11370}, {5604, 44635, 1}, {6762, 7174, 3640}, {7968, 45477, 1}, {8198, 8205, 55}, {10919, 10921, 6215}, {11497, 22756, 3}, {12594, 19050, 10041}, {12595, 19048, 10049}, {26342, 26343, 6}, {45423, 45729, 3299}, {45425, 45728, 3301}

Notes

See X3640 for a discussion of X3641.