X168

MITTENPUNKT OF EXCENTRAL TRIANGLE

X168 = X9-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_168 ]: Line [ J_a X_168 ] [ J_b X_168 ]: Line [ J_b X_168 ] [ J_c X_168 ]: Line [ J_c X_168 ] { 9, 164 }: Central Line L(9, 164) { 165, 166 }: Central Line L(165, 166) { 1, 173 }: Central Line L(1, 173) 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_9 = MITTENPUNKT (0.5110, 0.1615) X_164 = INCENTER OF EXCENTRAL TRIANGLE (0.4930, 0.1115) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_166 = GERGONNE POINT OF EXCENTRAL TRIANGLE (0.5156, 0.1554) X_1 = INCENTER (0.5714, 0.2333) X_173 = CONGRUENT ISOSCELIZERS POINT (0.5924, 0.2741) X_168 = MITTENPUNKT OF EXCENTRAL TRIANGLE (0.4565, 0.0098) A B C Ja Jb Jc X9 X164 X165 X166 X1 X173 X168 (a, b, c) = (5, 6, 7) | AB = 1

X168 (MITTENPUNKT OF EXCENTRAL TRIANGLE) 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–X168, Jb–X168, Jc–X168 concurring at X168

Trilinears: \(\sin A - \sin B - \sin C + 2[\cos A/2 + \sin(B/2 - A/2) + \sin(C/2 - A/2)] : :\)
Search Value (6, 9, 13): \(10.645890587226\)
▸ Alternate Coordinates1 form

  • Trilinears: \(b/(1 - \sin B/2) + c/(1 - \sin C/2) - a/(1 - \sin A/2) : :\)

▸ Incident Central Lines3 lines

{1, 173}, {9, 164}, {165, 166}

▸ Functional Relations5 relations