X1739

MIMOSA TRANSFORM OF X106

X1739 = crosspoint of X75 and X88
< 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) { 10, 38 }: Central Line L(10, 38) { 1, 474 }: Central Line L(1, 474) { 238, 484 }: Central Line L(238, 484) { 240, 522 }: Central Line L(240, 522) { 244, 519 }: Central Line L(244, 519) { 36, 1054 }: Central Line L(36, 1054) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_1 = INCENTER (0.5714, 0.2333) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1054 = 6th SHARYGIN POINT (1.4286, -0.2333) X_1739 = MIMOSA TRANSFORM OF X(106) (1.3810, 0.6999) A B C X75 X88 X10 X38 X1 X474 X238 X484 X240 X522 X244 X519 X36 X1054 X1739 (a, b, c) = (5, 6, 7) | AB = 1

X1739 (MIMOSA TRANSFORM 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X106
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.866059241327\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = b^{3} + c^{3} + ab^{2} + ac^{2} - 2bc^{2} - 2b^{2}c\) (M. Iliev, 5/13/07)

▸ Incident Central Lines10 lines

{1, 474}, {10, 38}, {36, 1054}, {46, 1707}, {238, 484}, {240, 522}, {244, 519}, {278, 1714}, {758, 899}, {986, 1698}

▸ Functional Relations2 relations