X170

X9-ALEPH CONJUGATE OF X9

X170 = X76-of-excentral triangle
< A B C >: Reference Triangle △ABC < J_a J_b J_c >: Excentral Triangle △J_a J_b J_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) [ J_a X_170 ]: Line [ J_a X_170 ] [ J_b X_170 ]: Line [ J_b X_170 ] [ J_c X_170 ]: Line [ J_c X_170 ] { 1, 7 }: Soddy Line { 43, 218 }: Central Line L(43, 218) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) J_a = A-Excenter J_a (1.2857, 0.5249) J_b = B-Excenter J_b (-0.2857, 0.6999) J_c = C-Excenter J_c (0.4286, -1.0498) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_170 = -ALEPH CONJUGATE OF X(9) (0.4465, -0.0557) A B C Ja Jb Jc X1 X7 X43 X218 X170 (a, b, c) = (5, 6, 7) | AB = 1

X170 (X9-ALEPH CONJUGATE OF X9) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

  • Derived Triangle: Excentral Triangle △JaJbJc — vertices Ja, Jb, Jc (Anticevian triangle of Incenter X1 (the three excenters))

  • Concurrence Lines: Ja–X170, Jb–X170, Jc–X170 concurring at X170

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = - (\tan A/2)\sec^{2}(A/2) + (\tan B/2)\sec^{2}(B/2) + (\tan C/2)\sec^{2}(C/2)\)
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): \(15.535109236316\)
▸ Incident Central Lines2 lines

{1, 7}, {43, 218}

▸ Functional Relations5 relations