X3476

INTERSECTION OF LINES X1X_4 AND X8X_56

X3476 = isogonal conjugate of X3478
< 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, 4 }: Incenter–Orthocenter Line { 8, 56 }: Central Line L(8, 56) { 7, 528 }: Central Line L(7, 528) { 57, 519 }: Central Line L(57, 519) { 329, 529 }: Central Line L(329, 529) { 2, 1319 }: Central Line L(2, 1319) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3478 = ISOGONAL CONJUGATE OF X(3476) (0.5577, 0.1884) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_8 = NAGEL POINT (0.4694, 0.1333) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_7 = GERGONNE POINT (0.5903, 0.2769) X_528 = DIRECTION OF VECTOR AX + BX + CX, where X = X(11) (1.0237, -0.1286) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_529 = DIRECTION OF VECTOR AX + BX + CX, where X = X(12) (0.8589, 0.6909) X_2 = CENTROID (0.5374, 0.2000) X_1319 = BEVAN-SCHRÖDER POINT (0.9524, 0.9331) X_3476 = INTERSECTION OF LINES X(1)X(4) AND X(8)X(56) (0.5835, 0.2814) A B C X3478 X1 X4 X8 X56 X7 X528 X57 X519 X329 X529 X2 X1319 X3476 (a, b, c) = (5, 6, 7) | AB = 1

X3476 (INTERSECTION OF LINES X1X_4 AND X8X_56) 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 \(f(A,B,C) = 2 - \cos A - \cos B - \cos C + \cos B \cos C\)
Barycentrics: \((3 a^{2} - 2 a (b + c) + (b + c)^{2})/(a - b - c) : :\)
Search Value (6, 9, 13): \(0.742793664392\)
▸ Incident Central Lines15 lines

{1, 4}, {2, 1319}, {7, 528}, {8, 56}, {10, 1420}, {12, 1388}, {43, 1450}, {57, 519}, {100, 1470}, {329, 529}, {381, 1387}, {604, 2345}, {952, 999}, {956, 1617}, {993, 2078}

▸ Functional Relations2 relations