X2745

SR(X104, X108)

X2745 = reflection of X2720 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) { 2720, 3 }: Central Line L(2720, 3) { 104, 521 }: Central Line L(104, 521) { 108, 517 }: Central Line L(108, 517) { 8, 1309 }: Central Line L(8, 1309) { 513, 1295 }: Central Line L(513, 1295) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2720 = SR(X(100), X(108)) (0.9103, 0.4054) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_521 = ISOGONAL CONJUGATE OF X(108) (1.1224, 0.1534) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_8 = NAGEL POINT (0.4694, 0.1333) X_1309 = COLLINGS TRANSFORM OF X(860) (0.4052, -0.3994) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_1295 = COLLINGS TRANSFORM OF X(123) (0.4680, -0.4072) X_2745 = SR(X(104), X(108)) (0.4623, 0.0742) A B C X2720 X3 X104 X521 X108 X517 X8 X1309 X513 X1295 X2745 (a, b, c) = (5, 6, 7) | AB = 1

X2745 (SR(X104, X108)) 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 = X104, U = X108
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(13.722625028718\)

X2745 lies on the circumcircle.

▸ Incident Central Lines9 lines

{3, 2720}, {8, 1309}, {40, 2222}, {104, 521}, {108, 517}, {109, 2077}, {513, 1295}, {997, 2728}, {1158, 2765}

▸ Functional Relations2 relations