X821

ISOGONAL CONJUGATE OF X820

X821 is the isogonal conjugate of X820.
< 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) { 158, 255 }: Central Line L(158, 255) { 243, 411 }: Central Line L(243, 411) { 774, 823 }: Central Line L(774, 823) 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_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_411 = EULER X(21)-2nd-SUBSTITUTION POINT (0.4414, -0.0514) X_774 = CROSSPOINT OF X(1) AND X(158) (0.6363, 0.3186) X_823 = ISOGONAL CONJUGATE OF X(822) (0.5623, 0.6035) X_821 = ISOGONAL CONJUGATE OF X(820) (0.5996, 0.4597) A B C X1 X158 X255 X243 X411 X774 X823 X821 (a, b, c) = (5, 6, 7) | AB = 1

X821 (ISOGONAL CONJUGATE OF X820) 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 \(f(A,B,C) = \sec^{2} A /(\cos^{2} B + \cos^{2} C)\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A)f(A,B,C)\)
Search Value (6, 9, 13): \(1.095032026161\)
▸ Incident Central Lines3 lines

{158, 255}, {243, 411}, {774, 823}

▸ Functional Relations3 relations