X3132

X18-CEVA CONJUGATE OF X6

X3132 = X18-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 { 15, 51 }: Central Line L(15, 51) { 16, 184 }: Central Line L(16, 184) { 18, 1608 }: Central Line L(18, 1608) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) 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_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_1608 = TCC-PERSPECTOR OF X(18) (0.3143, -0.7663) X_3132 = -CEVA CONJUGATE OF X(6) (0.4024, -0.1533) A B C X18 X6 X2 X3 X15 X51 X16 X184 X1608 X3132 (a, b, c) = (5, 6, 7) | AB = 1

X3132 (X18-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 \(x : y : z\) = X18 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): \(-6.266645763917\)
▸ Incident Central Lines4 lines

{2, 3}, {15, 51}, {16, 184}, {18, 1608}

▸ Functional Relations4 relations

Notes

As a point on the Euler line, X3132 has Shinagawa coefficients \((F + 3^{1/2}S, -E - F - 3^{1/2}S)\).