X2505

RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, SPIEKER CIRCLE}

X2505 = complement of X2976
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 2976 }: Central Line L(2, 2976) { 11, 244 }: Central Line L(11, 244) { 513, 2490 }: Central Line L(513, 2490) { 2487, 2496 }: Central Line L(2487, 2496) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_2976 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, AC-INCIRCLE} (0.6020, 0.9165) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-5.7092, 3.2243) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-3.9847, 4.4241) X_2496 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, SPIEKER CIRCLE} (-1.8622, 2.2579) X_2505 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, SPIEKER CIRCLE} (0.5051, -0.1583) A B C Ma Mb Mc X2 X2976 X11 X244 X513 X2490 X2487 X2496 X2505 (a, b, c) = (5, 6, 7) | AB = 1

X2505 (RADICAL CENTER OF {INCIRCLE, NINE-POINT 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 \(f(a,b,c) = bc(b - c)[2a^{3} - 5(b + c)a^{2} - (b + c)^{3} + 8a(b^{2} + c^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.648919956923\)
▸ Incident Central Lines3 lines

{11, 244}, {513, 2490}, {2487, 2496}

▸ Functional Relations1 relation