X3155

X485-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, 372 }: Central Line L(51, 372) { 184, 371 }: Central Line L(184, 371) { 157, 590 }: Central Line L(157, 590) { 154, 1151 }: Central Line L(154, 1151) { 493, 1976 }: Central Line L(493, 1976) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_485 = VECTEN POINT (0.5773, 0.2578) 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_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_157 = -OF-TANGENTIAL-TRIANGLE (0.5266, 0.3812) X_590 = ISOGONAL CONJUGATE OF X(588) (0.5615, 0.2258) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_1151 = ISOGONAL CONJUGATE OF X(1131) (0.5483, 0.1819) X_493 = 1st VAN LAMOEN HOMOTHETIC CENTER (0.5707, 0.2293) X_1976 = TRILINEAR POLE OF PU(39) (1.0272, -0.3962) X_3155 = -CEVA CONJUGATE OF X(6) (0.5562, 0.2492) A B C X485 X6 X2 X3 X51 X372 X184 X371 X157 X590 X154 X1151 X493 X1976 X3155 (a, b, c) = (5, 6, 7) | AB = 1

X3155 (X485-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 \(x : y : z\) = X485 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): \(0.933809674087\)
▸ Incident Central Lines7 lines

{2, 3}, {51, 372}, {154, 1151}, {157, 590}, {184, 371}, {485, 2351}, {493, 1976}

▸ Functional Relations1 relation

Notes

As a point on the Euler line, X3155 has Shinagawa coefficients \((F - S, -E - F + S)\).