X836

CROSSPOINT OF X1 AND X394

X836 is the crosspoint of X1 and X394.
< 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) { 37, 73 }: Central Line L(37, 73) { 1, 393 }: Central Line L(1, 393) { 820, 1100 }: Central Line L(820, 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_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_820 = CROSSPOINT OF X(1) AND X(255) (0.5413, 0.0659) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_836 = CROSSPOINT OF X(1) AND X(394) (0.5391, 0.0551) A B C X1 X394 X37 X73 X393 X820 X1100 X836 (a, b, c) = (5, 6, 7) | AB = 1

X836 (CROSSPOINT OF X1 AND X394) 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 \(f(A,B,C) = \sin B \sec^{2} B + \sin C \sec^{2} C\)
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): \(2.621417052429\)
▸ Incident Central Lines3 lines

{1, 393}, {37, 73}, {820, 1100}

▸ Functional Relations3 relations