X1706

EXSIMILICENTER(BEVAN CIRCLE, SPIEKER CIRCLE)

The insimilicenter of the Bevan and Spieker circles is X9.
< 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) { 4, 9 }: Orthocenter–Spieker Line { 8, 57 }: Central Line L(8, 57) { 65, 200 }: Central Line L(65, 200) { 84, 355 }: Central Line L(84, 355) { 1, 474 }: Central Line L(1, 474) { 46, 529 }: Central Line L(46, 529) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_8 = NAGEL POINT (0.4694, 0.1333) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_355 = FUHRMANN CENTER (0.5408, 0.2645) X_1 = INCENTER (0.5714, 0.2333) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_529 = DIRECTION OF VECTOR AX + BX + CX, where X = X(12) (0.8589, 0.6909) X_1706 = EXSIMILICENTER(BEVAN CIRCLE, SPIEKER CIRCLE) (0.5323, 0.2107) A B C X4 X9 X8 X57 X65 X200 X84 X355 X1 X474 X46 X529 X1706 (a, b, c) = (5, 6, 7) | AB = 1

X1706 (EXSIMILICENTER(BEVAN CIRCLE, SPIEKER CIRCLE)) 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 \(f(a,b,c) = bc[2(b + c) - a(\cos A - \cos B - \cos C + 1)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.568656133707\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{3} + a^{2}(b + c) - a(b + c)^{2} - (b + c)(b^{2} - 6bc + c^{2})\)

▸ Incident Central Lines19 lines

{1, 474}, {2, 1697}, {4, 9}, {8, 57}, {46, 529}, {65, 200}, {84, 355}, {165, 958}, {404, 1420}, {517, 936}, {1329, 1699}, {1377, 1702}, {1378, 1703}, {1571, 1573}, {1572, 1574}, {1678, 1704}, {1679, 1705}, {1680, 1700}, {1681, 1701}

▸ Functional Relations1 relation