X3504

INTERSECTION OF LINES X25X_385 AND X32X_1613

X3504 = isogonal cojugate of X3186
< 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) { 25, 385 }: Central Line L(25, 385) { 1423, 1716 }: Central Line L(1423, 1716) { 32, 3229 }: Central Line L(32, 3229) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_1423 = -BETH CONJUGATE OF X(192) (0.6537, 0.3692) X_1716 = MIMOSA TRANSFORM OF X(31) (0.8201, 0.4954) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_3229 = ISOGONAL CONJUGATE OF X(3225) (1.6061, 1.0091) X_3504 = INTERSECTION OF LINES X(25)X(385) AND X(32)X(1613) (0.2085, 0.0313) A B C X69 X3 X25 X385 X1423 X1716 X32 X3229 X3504 (a, b, c) = (5, 6, 7) | AB = 1

X3504 (INTERSECTION OF LINES X25X_385 AND X32X_1613) 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 \(f(a,b,c) = a(b^{2} + c^{2} - a^{2})/(b^{2}c^{2} - c^{2}a^{2} - a^{2}b^{2}) (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(10.713860481624\)

X3504 lies on the cubic Z(X385).

▸ Incident Central Lines3 lines

{25, 385}, {32, 3229}, {1423, 1716}

▸ Functional Relations6 relations