X1305

COLLINGS TRANSFORM OF X440

X1305 = reflection of X917 in X3
< 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) { 917, 3 }: Central Line L(917, 3) { 20, 103 }: Central Line L(20, 103) { 106, 347 }: Central Line L(106, 347) { 22, 675 }: Central Line L(22, 675) { 112, 653 }: Central Line L(112, 653) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_917 = -CROSS CONJUGATE OF X(4) (0.9795, 0.2766) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_22 = EXETER POINT (0.4143, -0.1221) X_675 = TRILINEAR POLE OF LINE X(6)X(514) (0.9212, -0.1860) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_1305 = COLLINGS TRANSFORM OF X(440) (0.0205, -0.0724) A B C X917 X3 X20 X103 X106 X347 X22 X675 X112 X653 X1305 (a, b, c) = (5, 6, 7) | AB = 1

X1305 (COLLINGS TRANSFORM OF X440) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1286)
Search Value (6, 9, 13): \(-0.594149458622\)

X1305 lies on the circumcircle.

▸ Incident Central Lines8 lines

{3, 917}, {20, 103}, {22, 675}, {106, 347}, {110, 664}, {112, 653}, {272, 759}, {915, 1006}

▸ Functional Relations6 relations