X3184

X20-CEVA CONJUGATE OF X30

X3184 = inverse-in-circumcircle of X2935
< 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) { 20, 107 }: Central Line L(20, 107) { 3, 113 }: Central Line L(3, 113) { 30, 133 }: Central Line L(30, 133) { 112, 376 }: Central Line L(112, 376) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_133 = INTERSECTION OF LINES X(4)X(74) AND X(5)X(122) (0.5928, 0.5014) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_3184 = -CEVA CONJUGATE OF X(30) (0.4805, 0.2077) A B C X20 X107 X3 X113 X30 X133 X112 X376 X3184 (a, b, c) = (5, 6, 7) | AB = 1

X3184 (X20-CEVA CONJUGATE OF X30) 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 \(x : y : z\) = X20 and \(u : v : w\) = X30
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): \(9.743351593627\)
▸ Incident Central Lines4 lines

{3, 113}, {20, 107}, {30, 133}, {112, 376}

▸ Functional Relations5 relations