X1613

TCC-PERSPECTOR OF X31

X1613 is the tcc-perspector of X31.
< 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, 6 }: Centroid–Symmedian Line { 154, 237 }: Central Line L(154, 237) { 3, 695 }: Central Line L(3, 695) { 25, 694 }: Central Line L(25, 694) { 110, 699 }: Central Line L(110, 699) { 305, 732 }: Central Line L(305, 732) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_699 = EVEN (- 4, - 2) CIRCUMCIRCLE POINT (0.9822, 0.2692) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_732 = EVEN (- 2, 2) INFINITY POINT (0.9745, 0.5915) X_1613 = TCC-PERSPECTOR OF X(31) (0.7015, 0.3763) A B C X2 X6 X154 X237 X3 X695 X25 X694 X110 X699 X305 X732 X1613 (a, b, c) = (5, 6, 7) | AB = 1

X1613 (TCC-PERSPECTOR OF X31) 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 \(f(a,b,c) = a(b^{2}c^{2} - c^{2}a^{2} - a^{2}b^{2})\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(-0.376969763844\)
▸ Incident Central Lines8 lines

{1, 1197}, {2, 6}, {3, 695}, {25, 694}, {110, 699}, {154, 237}, {305, 732}, {511, 1196}

▸ Functional Relations10 relations