X2765

SR(X108, X109)

X2765 = reflection of X2733 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) { 2733, 3 }: Central Line L(2733, 3) { 108, 522 }: Central Line L(108, 522) { 109, 521 }: Central Line L(109, 521) { 112, 1021 }: Central Line L(112, 1021) { 515, 1295 }: Central Line L(515, 1295) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2733 = SR(X(102), X(108)) (0.2875, -0.3619) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_521 = ISOGONAL CONJUGATE OF X(108) (1.1224, 0.1534) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_1021 = ISOGONAL CONJUGATE OF X(1020) (24.7475, -5.0780) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_1295 = COLLINGS TRANSFORM OF X(123) (0.4680, -0.4072) X_2765 = SR(X(108), X(109)) (0.7125, 0.5660) A B C X2733 X3 X108 X522 X109 X521 X112 X1021 X515 X1295 X2765 (a, b, c) = (5, 6, 7) | AB = 1

X2765 (SR(X108, X109)) 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 = X108, U = X109
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.971609115655\)

X2765 lies on the circumcircle.

▸ Incident Central Lines6 lines

{3, 2733}, {108, 522}, {109, 521}, {112, 1021}, {515, 1295}, {1158, 2745}

▸ Functional Relations3 relations