X2551

EXSIMILICENTER(SPIEKER CIRCLE, (X4,2R))

The circle (X4,2R) is identified at X2474.
< 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) { 1706, 10 }: Orthocenter–Spieker Line { 4, 9 }: Orthocenter–Spieker Line { 2, 12 }: Central Line L(2, 12) { 8, 210 }: Central Line L(8, 210) { 65, 329 }: Central Line L(65, 329) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1706 = EXSIMILICENTER(BEVAN CIRCLE, SPIEKER CIRCLE) (0.5323, 0.2107) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_2 = CENTROID (0.5374, 0.2000) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_8 = NAGEL POINT (0.4694, 0.1333) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_2551 = EXSIMILICENTER(SPIEKER CIRCLE, (X(4),2R)) (0.5086, 0.1559) A B C X1706 X10 X4 X9 X2 X12 X8 X210 X65 X329 X2551 (a, b, c) = (5, 6, 7) | AB = 1

X2551 (EXSIMILICENTER(SPIEKER CIRCLE, (X4,2R))) 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 \(f(a,b,c) = bc(b + c - a \cos B \cos C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.629141734303\)
▸ Incident Central Lines33 lines

{2, 12}, {3, 1603}, {4, 9}, {8, 210}, {20, 1376}, {55, 452}, {63, 1788}, {65, 329}, {200, 950}, {219, 387}, {220, 1834}, {318, 1857}, {377, 1155}, {390, 480}, {443, 1478}, {515, 936}, {518, 938}, {519, 1058}, {631, 993}, {944, 997}, {1056, 1125}, {1377, 1587}, {1378, 1588}, {1573, 2548}, {1574, 2549}, {1678, 2542}, {1679, 2543}, {1680, 2546}, {1681, 2547}, {2013, 2544}, {2014, 2545}, {2467, 2552}, {2468, 2553}

▸ Functional Relations2 relations