X2687

SR(X74, X100)

X2687 = reflection of X1290 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) { 1290, 3 }: Central Line L(1290, 3) { 30, 100 }: Central Line L(30, 100) { 108, 186 }: Central Line L(108, 186) { 21, 476 }: Central Line L(21, 476) { 74, 513 }: Central Line L(74, 513) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1290 = COLLINGS TRANSFORM OF X(36) (1.0092, 0.1355) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_186 = INVERSE-IN-CIRCUMCIRCLE OF X(4) (0.7957, 0.8758) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_476 = TIXIER POINT (0.9824, 0.2685) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_2687 = SR(X(74), X(100)) (-0.0092, 0.0687) A B C X1290 X3 X30 X100 X108 X186 X21 X476 X74 X513 X2687 (a, b, c) = (5, 6, 7) | AB = 1

X2687 (SR(X74, X100)) 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 = X74, U = X100
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(14.167194661565\)

X2687 lies on the circumcircle.

▸ Incident Central Lines16 lines

{3, 1290}, {4, 2766}, {21, 476}, {28, 1304}, {30, 100}, {35, 2222}, {65, 2720}, {74, 513}, {101, 2173}, {104, 523}, {107, 2074}, {108, 186}, {109, 484}, {110, 517}, {376, 2691}, {1006, 2690}

▸ Functional Relations5 relations