X1025

INTERSECTION OF LINES X2X_7 AND X100X_109

X1025 = trilinear pole of line X241X518
< 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) { 2, 7 }: Centroid–Gergonne Line { 100, 109 }: Central Line L(100, 109) { 190, 658 }: Central Line L(190, 658) { 644, 934 }: Central Line L(644, 934) { 664, 1018 }: Central Line L(664, 1018) { 813, 927 }: Central Line L(813, 927) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1024 = INTERSECTION OF LINES X(6)X(513) ANDX(9)X(522) (1.0370, 0.0294) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_658 = TRILINEAR POLE OF LINE X(1)X(7) (0.3795, 0.5837) X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA (-0.0171, 0.3359) X_934 = -CROSS CONJUGATE OF X(57) (0.4269, 0.6071) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_1018 = -CROSS CONJUGATE OF X(1) (0.1051, 0.4358) X_813 = o-(- 1, 1) CIRCUMCIRCLE POINT (0.9721, -0.0916) X_927 = ISOGONAL CONJUGATE OF X(926) (1.0037, 0.1836) X_1025 = INTERSECTION OF LINES X(2)X(7) AND X(100)X(109) (1.0996, 1.0180) A B C X1024 X2 X7 X100 X109 X190 X658 X644 X934 X664 X1018 X813 X927 X1025 (a, b, c) = (5, 6, 7) | AB = 1

X1025 (INTERSECTION OF LINES X2X_7 AND X100X_109) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = [b^{2} + c^{2} - a(b + c)]/[(b - c)(b + c - a)]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-0.537630169632\)
▸ Incident Central Lines7 lines

{2, 7}, {56, 1083}, {100, 109}, {190, 658}, {644, 934}, {664, 1018}, {813, 927}

▸ Functional Relations2 relations