X2096

REFLECTION OF X4 IN X57

X2096 is the reflection of X4 in X57.
< 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) { 4, 57 }: Central Line L(4, 57) { 7, 104 }: Central Line L(7, 104) { 20, 145 }: Central Line L(20, 145) { 3, 329 }: Central Line L(3, 329) { 376, 527 }: Central Line L(376, 527) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_7 = GERGONNE POINT (0.5903, 0.2769) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_527 = DIRECTION OF VECTOR AX + BX + CX, where X = X(7) (0.8698, 0.6836) X_2096 = REFLECTION OF X(4) IN X(57) (0.6153, 0.2263) A B C X4 X57 X7 X104 X20 X145 X3 X329 X376 X527 X2096 (a, b, c) = (5, 6, 7) | AB = 1

X2096 (REFLECTION OF X4 IN X57) 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) is as noted just above X2093
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.437529993962\)
▸ Incident Central Lines10 lines

{3, 329}, {4, 57}, {7, 104}, {20, 145}, {30, 2094}, {376, 527}, {388, 1158}, {515, 2093}, {1478, 1768}, {1503, 2097}

▸ Functional Relations2 relations