X1572

EXSIMILICENTER OF EXCENTRAL AND MOSES CIRCLES

X1572 is the exsimilicenter 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) { 1, 32 }: Central Line L(1, 32) { 39, 40 }: Central Line L(39, 40) { 6, 517 }: Central Line L(6, 517) { 165, 574 }: Central Line L(165, 574) { 57, 1015 }: Central Line L(57, 1015) { 9, 1573 }: Central Line L(9, 1573) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_40 = BEVAN POINT (0.4286, -0.0292) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_574 = HARMONIC OF X(187) (0.5539, 0.1910) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1015 = EXSIMILICENTER OF MOSES CIRCLE AND INCIRCLE (0.7982, 0.1348) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1573 = INSIMILICENTER OF SPIEKER AND MOSES CIRCLES (0.5399, 0.1993) X_1572 = EXSIMILICENTER OF EXCENTRAL AND MOSES CIRCLES (0.6204, 0.3047) A B C X1 X32 X39 X40 X6 X517 X165 X574 X57 X1015 X9 X1573 X1572 (a, b, c) = (5, 6, 7) | AB = 1

X1572 (EXSIMILICENTER OF EXCENTRAL AND MOSES CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(bcr + a^{2}R) : :\)
Search Value (6, 9, 13): \(0.435120739096\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(a^{3} + 4(\operatorname{area})r : :\), where r =inradius

  • Trilinears: \(sa^{3} + S^{2} : sb^{3} + S^{2} : sc^{3} + S^{2}\)

▸ Linear Combinations1 combination

  • X1572 = \(2\) X39 - \((\tan \omega \sin 2\omega )\) X40 = X1 - \(2\) X3 + \((2 \cot \omega \csc 2\omega )\) X39

▸ Incident Central Lines6 lines

{1, 32}, {6, 517}, {9, 1573}, {39, 40}, {57, 1015}, {165, 574}