X1290

COLLINGS TRANSFORM OF X36

X1290 = cevapoint of X36 and X513
< 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) { 1325, 36 }: Central Line L(1325, 36) { 23, 105 }: Central Line L(23, 105) { 30, 104 }: Central Line L(30, 104) { 74, 517 }: Central Line L(74, 517) { 100, 523 }: Central Line L(100, 523) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1325 = CIRCUMCIRCLE-INVERSE OF X(21) (1.6575, 3.1305) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_1290 = COLLINGS TRANSFORM OF X(36) (1.0092, 0.1355) A B C X1325 X36 X23 X105 X30 X104 X74 X517 X100 X523 X1290 (a, b, c) = (5, 6, 7) | AB = 1

X1290 (COLLINGS TRANSFORM OF X36) 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): \(-0.602468873173\)

X1290 lies on the circumcircle.

▸ Incident Central Lines10 lines

{23, 105}, {30, 104}, {36, 759}, {74, 517}, {99, 693}, {100, 523}, {101, 661}, {110, 513}, {186, 915}, {354, 840}

▸ Functional Relations7 relations