X3176

X8-CEVA CONJUGATE OF X4

X3176 = X8-Ceva conjugate of X4
< 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) { 4, 65 }: Central Line L(4, 65) { 1, 281 }: Central Line L(1, 281) { 20, 653 }: Central Line L(20, 653) { 92, 938 }: Central Line L(92, 938) { 8, 1034 }: Central Line L(8, 1034) { 278, 1210 }: Central Line L(278, 1210) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1 = INCENTER (0.5714, 0.2333) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_938 = ANTICOMPLEMENT OF X(936) (0.5846, 0.2462) X_1034 = -CROSS CONJUGATE OF X(8) (0.3920, -0.4271) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_1210 = ISOGONAL CONJUGATE OF X(1167) (0.6144, 0.2754) X_3176 = -CEVA CONJUGATE OF X(4) (0.7574, 2.2179) A B C X8 X4 X65 X1 X281 X20 X653 X92 X938 X1034 X278 X1210 X3176 (a, b, c) = (5, 6, 7) | AB = 1

X3176 (X8-CEVA CONJUGATE OF X4) 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 \(x : y : z\) = X8 and \(u : v : w\) = X4
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): \(1.015772993281\)
▸ Incident Central Lines12 lines

{1, 281}, {4, 65}, {8, 1034}, {20, 653}, {40, 1712}, {84, 1767}, {92, 938}, {207, 1490}, {243, 1788}, {278, 1210}, {451, 3085}, {1863, 1902}

▸ Functional Relations1 relation