X1423

X192-BETH CONJUGATE OF X192

X1423 = X56-Ceva conjugate of X57
< 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) { 2, 7 }: Centroid–Gergonne Line { 56, 87 }: Central Line L(56, 87) { 1, 256 }: Central Line L(1, 256) { 269, 292 }: Central Line L(269, 292) { 65, 984 }: Central Line L(65, 984) { 604, 651 }: Central Line L(604, 651) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_1 = INCENTER (0.5714, 0.2333) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_1423 = -BETH CONJUGATE OF X(192) (0.6537, 0.3692) A B C X192 X2 X7 X56 X87 X1 X256 X269 X292 X65 X984 X604 X651 X1423 (a, b, c) = (5, 6, 7) | AB = 1

X1423 (X192-BETH CONJUGATE OF X192) 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 \(f(a,b,c) = (ab + ac - bc)/(b + c - a)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.044113636441\)
▸ Incident Central Lines11 lines

{1, 256}, {2, 7}, {6, 1429}, {43, 1403}, {56, 87}, {65, 984}, {85, 1221}, {241, 1122}, {269, 292}, {604, 651}, {1201, 1419}

▸ Functional Relations7 relations