X1417

X106-BETH CONJUGATE OF X106

X1417 = isogonal conjugate of X4723
< 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) { 56, 106 }: Central Line L(56, 106) { 88, 961 }: Central Line L(88, 961) { 65, 1320 }: Central Line L(65, 1320) { 604, 1415 }: Central Line L(604, 1415) { 1014, 1122 }: Central Line L(1014, 1122) { 901, 1319 }: Central Line L(901, 1319) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_961 = ISOGONAL CONJUGATE OF X(960) (0.6167, 0.3210) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1320 = ISOGONAL CONJUGATE OF X(1319) (1.0000, 0.0000) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_1415 = -BETH CONJUGATE OF X(101) (0.4138, 0.6170) X_1014 = ISOGONAL CONJUGATE OF X(210) (0.6222, 0.3285) X_1122 = 1st GRINBERG POINT (0.6289, 0.3227) X_901 = ISOGONAL CONJUGATE OF X(900) (1.0000, -0.0000) X_1319 = BEVAN-SCHRÖDER POINT (0.9524, 0.9331) X_1417 = -BETH CONJUGATE OF X(106) (1.0000, 0.0000) A B C X106 X56 X88 X961 X65 X1320 X604 X1415 X1014 X1122 X901 X1319 X1417 (a, b, c) = (5, 6, 7) | AB = 1

X1417 (X106-BETH CONJUGATE OF X106) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X106
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.415752900463\)
▸ Incident Central Lines7 lines

{56, 106}, {65, 1320}, {88, 961}, {604, 1415}, {901, 1319}, {1014, 1122}, {1037, 1470}

▸ Functional Relations1 relation

  • X1417 = isogonal conjugate of X4723