X2769

SR(X109, X112)

X2769 = isogonal conjugate of X2853
< 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) { 109, 525 }: Central Line L(109, 525) { 112, 522 }: Central Line L(112, 522) { 102, 1503 }: Central Line L(102, 1503) { 108, 1577 }: Central Line L(108, 1577) { 515, 1297 }: Central Line L(515, 1297) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2853 = ISOGONAL CONJUGATE OF X(2769) (1.1201, 0.2698) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_1503 = POINT ARKAB (0.4818, -0.3843) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_1577 = ISOGONAL CONJUGATE OF X(163) (-17.7211, 5.4989) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_1297 = COLLINGS TRANSFORM OF X(127) (0.4838, -0.4080) X_2769 = SR(X(109), X(112)) (0.7268, 0.5592) A B C X2853 X109 X525 X112 X522 X102 X1503 X108 X1577 X515 X1297 X2769 (a, b, c) = (5, 6, 7) | AB = 1

X2769 (SR(X109, X112)) 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 given just before X2677 using P = X109, U = X112
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.228831554861\)

X2769 lies on the circumcircle.

▸ Incident Central Lines5 lines

{102, 1503}, {108, 1577}, {109, 525}, {112, 522}, {515, 1297}

▸ Functional Relations1 relation