X2005

ORTHOCORRESPONDENT OF X62

< 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, 14 }: Central Line L(2, 14) { 51, 62 }: Central Line L(51, 62) { 32, 2004 }: Central Line L(32, 2004) 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_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_2004 = ORTHOCORRESPONDENT OF X(61) (0.6075, 0.3138) X_2005 = ORTHOCORRESPONDENT OF X(62) (0.4874, 0.2417) A B C X2 X14 X51 X62 X32 X2004 X2005 (a, b, c) = (5, 6, 7) | AB = 1

X2005 (ORTHOCORRESPONDENT OF X62) 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 \(x : y : z\) = X62
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.403820031208\)
▸ Incident Central Lines3 lines

{2, 14}, {32, 2004}, {51, 62}