X1574

EXSIMILICENTER OF SPIEKER AND MOSES CIRCLES

X1574 is the exsimilicenter of Spieker and moses circles.
< 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) { 10, 39 }: Central Line L(10, 39) { 38, 762 }: Central Line L(38, 762) { 8, 1015 }: Central Line L(8, 1015) { 213, 899 }: Central Line L(213, 899) { 32, 1376 }: Central Line L(32, 1376) { 115, 1329 }: Central Line L(115, 1329) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_762 = TRILINEAR CUBE OF X(37) (0.5240, 0.1822) X_8 = NAGEL POINT (0.4694, 0.1333) X_1015 = EXSIMILICENTER OF MOSES CIRCLE AND INCIRCLE (0.7982, 0.1348) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_899 = INTERSECTION OF LINES X(1)X(2) AND X(6)X(750) (2.3571, 1.9829) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_1376 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE) (0.5265, 0.2074) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4903, 0.1280) X_1574 = EXSIMILICENTER OF SPIEKER AND MOSES CIRCLES (0.4596, 0.1333) A B C X10 X39 X38 X762 X8 X1015 X213 X899 X32 X1376 X115 X1329 X1574 (a, b, c) = (5, 6, 7) | AB = 1

X1574 (EXSIMILICENTER OF SPIEKER AND MOSES CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(b^{2} + c^{2}) - 2bc(b + c) : :\)
Search Value (6, 9, 13): \(5.193252493232\)
▸ Linear Combinations1 combination

  • X1574 = \((2R \tan \omega \sin 2\omega )\) X10 - \(r\) X39 = \(R\) X1 + \(R\) X8 - \((r \cot \omega \csc 2\omega )\) X39

▸ Incident Central Lines10 lines

{2, 1500}, {8, 1015}, {10, 39}, {32, 1376}, {38, 762}, {115, 1329}, {213, 899}, {574, 993}, {1377, 1504}, {1378, 1505}