X1571

INSIMILICENTER OF EXCENTRAL AND MOSES CIRCLES

X1571 is the insimilicenter of excentral 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) { 39, 40 }: Central Line L(39, 40) { 32, 165 }: Central Line L(32, 165) { 1, 574 }: Central Line L(1, 574) { 57, 1500 }: Central Line L(57, 1500) { 9, 1574 }: Central Line L(9, 1574) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_40 = BEVAN POINT (0.4286, -0.0292) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_1 = INCENTER (0.5714, 0.2333) X_574 = HARMONIC OF X(187) (0.5539, 0.1910) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1500 = INSIMILICENTER OF MOSES CIRCLE AND INCIRCLE (0.5747, 0.2319) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1574 = EXSIMILICENTER OF SPIEKER AND MOSES CIRCLES (0.4596, 0.1333) X_1571 = INSIMILICENTER OF EXCENTRAL AND MOSES CIRCLES (0.5507, 0.1833) A B C X39 X40 X32 X165 X1 X574 X57 X1500 X9 X1574 X1571 (a, b, c) = (5, 6, 7) | AB = 1

X1571 (INSIMILICENTER OF EXCENTRAL AND MOSES CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a[bcr + (a^{2} - 2b^{2} - 2c^{2})R] : :\), where R = circumradius, r = inradius
Search Value (6, 9, 13): \(2.490881038285\)
▸ Linear Combinations1 combination

  • X1571 = \(2\) X39 + \((\tan \omega \sin 2\omega )\) X40 = X1 - \(2\) X3 - \((2 \cot \omega \csc 2\omega )\) X39

▸ Incident Central Lines5 lines

{1, 574}, {9, 1574}, {32, 165}, {39, 40}, {57, 1500}