X3687

X171com(EXTOUCH TRIANGLE)

X3687 = excentral-to-ABC barycentric image of X171
< 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 { 57, 69 }: Central Line L(57, 69) { 75, 226 }: Central Line L(75, 226) { 9, 345 }: Central Line L(9, 345) { 261, 284 }: Central Line L(261, 284) { 63, 573 }: Central Line L(63, 573) 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_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_9 = MITTENPUNKT (0.5110, 0.1615) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_573 = ORTHOHARMONIC OF X(58) (0.4486, 0.0172) X_3687 = com(EXTOUCH TRIANGLE) (0.4619, 0.1260) A B C X1 X2 X57 X69 X75 X226 X9 X345 X261 X284 X63 X573 X3687 (a, b, c) = (5, 6, 7) | AB = 1

X3687 (X171com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (-a + b + c)(b^{2} + c^{2} + ab + ac)\)
Search Value (6, 9, 13): \(4.593379018585\)
▸ Incident Central Lines23 lines

{1, 2}, {9, 345}, {57, 69}, {63, 573}, {72, 970}, {75, 226}, {181, 518}, {261, 284}, {312, 2321}, {318, 469}, {319, 2985}, {320, 553}, {321, 908}, {355, 2050}, {440, 2968}, {914, 1150}, {950, 1043}, {960, 1682}, {1211, 2092}, {1376, 1460}, {1738, 2887}, {1812, 2323}, {2895, 3218}

▸ Functional Relations1 relation

  • X3687 = excentral-to-ABC barycentric image of X171