X2367

CIR(X32)

X2367 = isogonal conjugate of X2387
< 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) { 76, 110 }: Central Line L(76, 110) { 99, 160 }: Central Line L(99, 160) { 112, 264 }: Central Line L(112, 264) { 101, 313 }: Central Line L(101, 313) { 109, 349 }: Central Line L(109, 349) { 316, 805 }: Central Line L(316, 805) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2387 = ISOGONAL CONJUGATE OF X(2367) (0.6246, 0.4244) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_99 = STEINER POINT (0.1109, 0.4322) X_160 = -OF-TANGENTIAL-TRIANGLE (0.4841, -0.0647) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_349 = ISOTOMIC CONJUGATE OF X(284) (0.5089, 0.1906) X_316 = DROUSSENT PIVOT (-0.7850, -1.9118) X_805 = o-(- 2, 2) CIRCUMCIRCLE POINT (0.9729, -0.0897) X_2367 = CIR(X(32)) (0.7086, -0.3637) A B C X2387 X76 X110 X99 X160 X112 X264 X101 X313 X109 X349 X316 X805 X2367 (a, b, c) = (5, 6, 7) | AB = 1

X2367 (CIR(X32)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(F(u,v,w) : F(v,w,u) : F(w,u,v)\), where F is as indicated just before X2365, and \(u : v : w\) = X32.
Barycentrics: \(aF(u,v,w) : bF(v,w,u) : cF(w,u,v)\)
Search Value (6, 9, 13): \(13.648164698336\)

X2367 lies on the circumcircle.

▸ Incident Central Lines8 lines

{76, 110}, {99, 160}, {101, 313}, {109, 349}, {112, 264}, {276, 933}, {308, 827}, {316, 805}

▸ Functional Relations2 relations