X820

CROSSPOINT OF X1 AND X255

X820 is the crosspoint of X1 and X255.
< 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, 29 }: Central Line L(1, 29) { 3, 296 }: Central Line L(3, 296) { 662, 775 }: Central Line L(662, 775) { 836, 1100 }: Central Line L(836, 1100) 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_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_296 = ISOGONAL CONJUGATE OF X(243) (0.7214, -0.0918) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_775 = ISOGONAL CONJUGATE OF X(774) (0.4699, 0.1510) X_836 = CROSSPOINT OF X(1) AND X(394) (0.5391, 0.0551) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_820 = CROSSPOINT OF X(1) AND X(255) (0.5413, 0.0659) A B C X1 X255 X29 X3 X296 X662 X775 X836 X1100 X820 (a, b, c) = (5, 6, 7) | AB = 1

X820 (CROSSPOINT OF X1 AND X255) 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 \(f(A,B,C) = \cos^{2} A (\cos^{2} B + \cos^{2} C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.304798246387\)
▸ Incident Central Lines4 lines

{1, 29}, {3, 296}, {662, 775}, {836, 1100}

▸ Functional Relations3 relations