X3166

X3-CEVA CONJUGATE OF X16

X3166 = X3-Ceva conjugate of X16
< 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, 61 }: Central Line L(54, 61) { 15, 184 }: Central Line L(15, 184) { 16, 186 }: Central Line L(16, 186) { 35, 1095 }: Central Line L(35, 1095) { 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_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_54 = KOSNITA POINT (0.5880, 0.2176) X_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) 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_1095 = TRILINEAR SQUARE OF X(16) (0.4127, 0.3906) X_577 = HARMONIC OF X(216) (0.4663, 0.0464) X_3165 = -CEVA CONJUGATE OF X(15) (0.4755, -0.0277) X_3166 = -CEVA CONJUGATE OF X(16) (0.4265, 0.3664) A B C X3 X16 X54 X61 X15 X184 X186 X35 X1095 X577 X3165 X3166 (a, b, c) = (5, 6, 7) | AB = 1

X3166 (X3-CEVA CONJUGATE OF X16) 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 \(u : v : w\) = X16
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): \(2.298435159747\)
▸ Incident Central Lines5 lines

{15, 184}, {16, 186}, {35, 1095}, {54, 61}, {577, 3165}

▸ Functional Relations1 relation