X3156

X486-CEVA CONJUGATE OF X6

< 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, 3 }: Euler Line { 51, 371 }: Central Line L(51, 371) { 184, 372 }: Central Line L(184, 372) { 157, 615 }: Central Line L(157, 615) { 154, 1152 }: Central Line L(154, 1152) { 494, 1976 }: Central Line L(494, 1976) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_157 = -OF-TANGENTIAL-TRIANGLE (0.5266, 0.3812) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_1152 = ISOGONAL CONJUGATE OF X(1132) (-0.9520, -2.2961) X_494 = 2nd VAN LAMOEN HOMOTHETIC CENTER (3.0897, 0.6637) X_1976 = TRILINEAR POLE OF PU(39) (1.0272, -0.3962) X_3156 = -CEVA CONJUGATE OF X(6) (0.1342, -0.8550) A B C X486 X6 X2 X3 X51 X371 X184 X372 X157 X615 X154 X1152 X494 X1976 X3156 (a, b, c) = (5, 6, 7) | AB = 1

X3156 (X486-CEVA CONJUGATE OF X6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X486 and \(u : v : w\) = X6
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(-3.029762355751\)
▸ Incident Central Lines7 lines

{2, 3}, {51, 371}, {154, 1152}, {157, 615}, {184, 372}, {486, 2351}, {494, 1976}

▸ Functional Relations1 relation

Notes

As a point on the Euler line, X3156 has Shinagawa coefficients \((F + S, -E - F - S)\).