X2751

SR(X105, X109)

X2751 = reflection of X2730 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) { 2730, 3 }: Central Line L(2730, 3) { 105, 522 }: Central Line L(105, 522) { 109, 518 }: Central Line L(109, 518) { 9, 919 }: Central Line L(9, 919) { 63, 901 }: Central Line L(63, 901) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2730 = SR(X(102), X(105)) (1.0078, 0.0514) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_9 = MITTENPUNKT (0.5110, 0.1615) X_919 = ISOGONAL CONJUGATE OF X(918) (1.0058, 0.1699) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_901 = ISOGONAL CONJUGATE OF X(900) (1.0000, -0.0000) X_2751 = SR(X(105), X(109)) (-0.0078, 0.1527) A B C X2730 X3 X105 X522 X109 X518 X9 X919 X63 X901 X2751 (a, b, c) = (5, 6, 7) | AB = 1

X2751 (SR(X105, 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 = X105, U = X109
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(11.383941674633\)

X2751 lies on the circumcircle.

▸ Incident Central Lines11 lines

{3, 2730}, {9, 919}, {63, 901}, {75, 927}, {105, 522}, {106, 905}, {108, 1861}, {109, 518}, {515, 1292}, {956, 1308}, {1376, 2222}

▸ Functional Relations2 relations