X3165

X3-CEVA CONJUGATE OF X15

X3165 = X3-Ceva conjugate of X15
< 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) { 54, 62 }: Central Line L(54, 62) { 16, 184 }: Central Line L(16, 184) { 15, 186 }: Central Line L(15, 186) { 35, 1094 }: Central Line L(35, 1094) { 577, 3165 }: Central Line L(577, 3165) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_54 = KOSNITA POINT (0.5880, 0.2176) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_186 = INVERSE-IN-CIRCUMCIRCLE OF X(4) (0.7957, 0.8758) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_1094 = TRILINEAR SQUARE OF X(15) (0.5301, 0.1475) X_577 = HARMONIC OF X(216) (0.4663, 0.0464) X_3165 = -CEVA CONJUGATE OF X(15) (0.4755, -0.0277) A B C X3 X15 X54 X62 X16 X184 X186 X35 X1094 X577 X3165 (a, b, c) = (5, 6, 7) | AB = 1

X3165 (X3-CEVA CONJUGATE OF X15) 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 \(x : y : z\) = X3 and \(u : v : w\) = X15
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): \(-11.524307321547\)
▸ Incident Central Lines5 lines

{15, 186}, {16, 184}, {35, 1094}, {54, 62}, {577, 3165}

▸ Functional Relations1 relation