X2000

ORTHOCORRESPONDENT OF X19

< 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) { 1, 2 }: Nagel Line { 33, 63 }: Central Line L(33, 63) { 241, 1004 }: Central Line L(241, 1004) { 9, 1331 }: Central Line L(9, 1331) { 75, 1897 }: Central Line L(75, 1897) { 169, 1995 }: Central Line L(169, 1995) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_1004 = INTERCEPT OF EULER LINE AND LINE X(7)X(100) (0.5701, 0.2854) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1331 = ORTHOCORRESPONDENT OF X(101) (-0.2308, 0.2512) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1897 = ZOSMA TRANSFORM OF X(1054) (0.4360, 0.5756) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_1995 = ORTHOCORRESPONDENT OF X(6) (0.5718, 0.2899) X_2000 = ORTHOCORRESPONDENT OF X(19) (0.4996, 0.1629) A B C X1 X2 X33 X63 X241 X1004 X9 X1331 X75 X1897 X169 X1995 X2000 (a, b, c) = (5, 6, 7) | AB = 1

X2000 (ORTHOCORRESPONDENT OF X19) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = yz + (-x \cos A + y \cos B + z \cos C)x\), where \(x : y : z\) = X19
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.267096662594\)
▸ Incident Central Lines6 lines

{1, 2}, {9, 1331}, {33, 63}, {75, 1897}, {169, 1995}, {241, 1004}