X2004

ORTHOCORRESPONDENT OF X61

< 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, 13 }: Central Line L(2, 13) { 51, 61 }: Central Line L(51, 61) { 32, 2005 }: Central Line L(32, 2005) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_2005 = ORTHOCORRESPONDENT OF X(62) (0.4874, 0.2417) X_2004 = ORTHOCORRESPONDENT OF X(61) (0.6075, 0.3138) A B C X2 X13 X51 X61 X32 X2005 X2004 (a, b, c) = (5, 6, 7) | AB = 1

X2004 (ORTHOCORRESPONDENT OF X61) 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 \(x : y : z\) = X61
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.523531492113\)
▸ Incident Central Lines3 lines

{2, 13}, {32, 2005}, {51, 61}