X1573

INSIMILICENTER OF SPIEKER AND MOSES CIRCLES

X1573 is the insimilicenter 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) { 37, 519 }: Central Line L(37, 519) { 75, 538 }: Central Line L(75, 538) { 2, 668 }: Central Line L(2, 668) { 32, 958 }: Central Line L(32, 958) { 187, 993 }: Central Line L(187, 993) 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_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_538 = DIRECTION OF VECTOR AX + BX + CX, where X = X(39) (1.0053, 0.5542) X_2 = CENTROID (0.5374, 0.2000) X_668 = TRILINEAR POLE OF LINE X(2)X(37) (0.0159, 0.3302) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_993 = MIDPOINT OF X(1) AND X(63) (0.5140, 0.1578) X_1573 = INSIMILICENTER OF SPIEKER AND MOSES CIRCLES (0.5399, 0.1993) A B C X10 X39 X37 X519 X75 X538 X2 X668 X32 X958 X187 X993 X1573 (a, b, c) = (5, 6, 7) | AB = 1

X1573 (INSIMILICENTER 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): \(2.537384777539\)
▸ Linear Combinations1 combination

  • X1573 = \((2R \tan \omega \sin 2\omega )\) X10 + \(r\) X39 = \(R\) X1 + \(R\) X8 + \((r \cot \omega \csc 2\omega )\) X39

▸ Incident Central Lines11 lines

{2, 668}, {8, 1500}, {10, 39}, {32, 958}, {37, 519}, {75, 538}, {187, 993}, {574, 1376}, {1329, 1508}, {1377, 1505}, {1378, 1504}