X3719

X1711com(EXTOUCH TRIANGLE)

X3719 = excentral-to-ABC barycentric image of X1711
< 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) { 63, 69 }: Central Line L(63, 69) { 78, 212 }: Central Line L(78, 212) { 9, 312 }: Central Line L(9, 312) { 326, 394 }: Central Line L(326, 394) { 271, 1265 }: Central Line L(271, 1265) { 740, 1711 }: Central Line L(740, 1711) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_9 = MITTENPUNKT (0.5110, 0.1615) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_326 = ISOTOMIC CONJUGATE OF X(158) (0.3354, 0.0219) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_271 = ISOGONAL CONJUGATE OF X(208) (1.1546, 2.8606) X_1265 = ISOTOMIC CONJUGATE OF X(1119) (0.2751, 0.0213) X_740 = EVEN (- 1, 1) INFINITY POINT (0.9745, 0.5915) X_1711 = MIMOSA TRANSFORM OF X(19) (0.8600, 0.5386) X_3719 = com(EXTOUCH TRIANGLE) (0.2722, 0.0121) A B C X63 X69 X78 X212 X9 X312 X326 X394 X271 X1265 X740 X1711 X3719 (a, b, c) = (5, 6, 7) | AB = 1

X3719 (X1711com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cot(A/2) \cot^{2} A : \cot(B/2) \cot^{2} B : \cot(C/2) \cot^{2} C\) (Peter Moses, 12/19/11)
Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b + c - a)(b^{2} + c^{2} - a^{2})^{2}\)
Search Value (6, 9, 13): \(5.927534644136\)
▸ Incident Central Lines10 lines

{9, 312}, {63, 69}, {78, 212}, {100, 2365}, {271, 1265}, {326, 394}, {346, 3219}, {740, 1711}, {2185, 3601}, {2269, 2339}

▸ Functional Relations1 relation

  • X3719 = excentral-to-ABC barycentric image of X1711