X1295

COLLINGS TRANSFORM OF X123

X1295 = cevapoint of X3 and X517
< 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) { 3, 108 }: Central Line L(3, 108) { 20, 100 }: Central Line L(20, 100) { 4, 123 }: Central Line L(4, 123) { 21, 107 }: Central Line L(21, 107) { 40, 109 }: Central Line L(40, 109) { 268, 281 }: Central Line L(268, 281) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_4 = ORTHOCENTER (0.6122, 0.3958) X_123 = -OF-MEDIAL-TRIANGLE (0.5401, -0.0057) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_40 = BEVAN POINT (0.4286, -0.0292) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_268 = ISOGONAL CONJUGATE OF X(196) (0.7710, 1.5678) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_1295 = COLLINGS TRANSFORM OF X(123) (0.4680, -0.4072) A B C X3 X108 X20 X100 X4 X123 X21 X107 X40 X109 X268 X281 X1295 (a, b, c) = (5, 6, 7) | AB = 1

X1295 (COLLINGS TRANSFORM OF X123) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1286)
Search Value (6, 9, 13): \(13.646486521278\)

X1295 lies on the circumcircle.

▸ Incident Central Lines9 lines

{3, 108}, {4, 123}, {20, 100}, {21, 107}, {28, 1301}, {40, 109}, {101, 610}, {268, 281}, {347, 934}

▸ Functional Relations13 relations