X1318

ISOGONAL CONJUGATE OF X1317

X1318 is the isogonal conjugate of X1317.
< 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) { 36, 106 }: Central Line L(36, 106) { 88, 517 }: Central Line L(88, 517) { 1, 1168 }: Central Line L(1, 1168) { 679, 1319 }: Central Line L(679, 1319) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1317 = REFLECTION OF X(11) IN X(1) (0.4082, 0.3999) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1 = INCENTER (0.5714, 0.2333) X_1168 = 1st SARAGOSSA POINT OF X(36) (1.0000, 0.0000) X_679 = ISOGONAL CONJUGATE OF X(678) (1.0000, 0.0000) X_1319 = BEVAN-SCHRÖDER POINT (0.9524, 0.9331) X_1318 = ISOGONAL CONJUGATE OF X(1317) (1.0000, 0.0000) A B C X1317 X36 X106 X88 X517 X1 X1168 X679 X1319 X1318 (a, b, c) = (5, 6, 7) | AB = 1

X1318 (ISOGONAL CONJUGATE OF X1317) 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 \(f(a,b,c) = a(b + c - a)/(b + c - 2a)^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.055507060842\)
▸ Incident Central Lines4 lines

{1, 1168}, {36, 106}, {88, 517}, {679, 1319}