X1485

PERSPECTOR OF ABC AND TANGENTIAL-OF-TANGENTIAL TRIANGLE

X1485 is the perspector of ABC and tangential-of-tangential triangle.
< 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) circumcircle: Circumcircle of △ABC { 22, 160 }: Central Line L(22, 160) { 26, 206 }: Central Line L(26, 206) { 157, 264 }: Central Line L(157, 264) { 232, 571 }: Central Line L(232, 571) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_22 = EXETER POINT (0.4143, -0.1221) X_160 = -OF-TANGENTIAL-TRIANGLE (0.4841, -0.0647) X_26 = CIRCUMCENTER OF THE TANGENTIAL TRIANGLE (0.1382, -0.8447) X_206 = -CEVA CONJUGATE OF X(32) (0.5105, -0.2297) X_157 = -OF-TANGENTIAL-TRIANGLE (0.5266, 0.3812) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_232 = -CEVA CONJUGATE OF X(132) (0.6919, 0.7779) X_571 = ORTHOHARMONIC OF X(52) (0.7141, 0.4556) X_1485 = PERSPECTOR OF ABC AND TANGENTIAL-OF-TANGENTIAL TRIANGLE (0.7356, 0.1420) A B C X3 X22 X160 X26 X206 X157 X264 X232 X571 X1485 (a, b, c) = (5, 6, 7) | AB = 1

X1485 (PERSPECTOR OF ABC AND TANGENTIAL-OF-TANGENTIAL TRIANGLE) 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 \(f(a,b,c) = a/(b^{3}\cos B + c^{3}\cos C - a^{3}\cos A)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(24.124270100258\)
▸ Incident Central Lines4 lines

{22, 160}, {26, 206}, {157, 264}, {232, 571}

▸ Functional Relations1 relation

Notes

Let HaHbHc be the orthic triangle. Let La be the reflection of line HbHc in the perpedicular bisector of BC, and define Lb and Lc cyclically. Let A″ = Lb∩Lc, B″ = Lc∩La, C″ = La∩Lb. The lines AA″, BB″, CC″ concur in X1485. (Randy Hutson, July 31 2018)