X1609

TCC-PERSPECTOR OF X19

X1609 is the tcc-perspector of X19.
< 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) { 3, 6 }: Brocard Axis { 25, 53 }: Central Line L(25, 53) { 24, 254 }: Central Line L(24, 254) { 159, 237 }: Central Line L(159, 237) { 48, 1195 }: Central Line L(48, 1195) { 112, 1299 }: Central Line L(112, 1299) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_249 = ISOGONAL CONJUGATE OF X(115) (0.5045, 0.3948) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_254 = -CROSS CONJUGATE OF X(4) (1.4506, 0.5587) X_159 = -OF-TANGENTIAL-TRIANGLE (0.4211, -0.7266) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_1195 = 3rd SARAGOSSA POINT OF X(19) (0.6245, 0.2796) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_1299 = COLLINGS TRANSFORM OF X(135) (0.7905, 0.5216) X_1609 = TCC-PERSPECTOR OF X(19) (0.7601, 0.5316) A B C X107 X249 X3 X6 X25 X53 X24 X254 X159 X237 X48 X1195 X112 X1299 X1609 (a, b, c) = (5, 6, 7) | AB = 1

X1609 (TCC-PERSPECTOR OF X19) 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 X1601)
Search Value (6, 9, 13): \(0.031584913625\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a(\cos^{2} B + \cos^{2} C - \cos^{2} A) : :\)

▸ Incident Central Lines9 lines

{3, 6}, {24, 254}, {25, 53}, {48, 1195}, {112, 1299}, {159, 237}, {186, 1249}, {590, 1583}, {615, 1584}

▸ Functional Relations5 relations