X1311

COLLINGS TRANSFORM OF X1146

X1311 = trilinear pole of line X6X522
< 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) { 8, 101 }: Central Line L(8, 101) { 2, 109 }: Central Line L(2, 109) { 29, 112 }: Central Line L(29, 112) { 92, 108 }: Central Line L(92, 108) { 100, 312 }: Central Line L(100, 312) { 110, 333 }: Central Line L(110, 333) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_2 = CENTROID (0.5374, 0.2000) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_1311 = COLLINGS TRANSFORM OF X(1146) (0.7713, -0.3301) A B C X8 X101 X2 X109 X29 X112 X92 X108 X100 X312 X110 X333 X1311 (a, b, c) = (5, 6, 7) | AB = 1

X1311 (COLLINGS TRANSFORM OF X1146) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(1/(a^{2} (b^{2} + c^{2}) - a b c (b + c) - (b - c)^{2} (b^{2} + b c + c^{2})) : :\)
Search Value (6, 9, 13): \(14.004957080781\)

X1311 lies on the circumcircle.

▸ Incident Central Lines8 lines

{2, 109}, {8, 101}, {29, 112}, {85, 934}, {92, 108}, {100, 312}, {110, 333}, {411, 1292}

▸ Functional Relations6 relations