X2976

RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, AC-INCIRCLE}

X2976 = anticomplement of X2505
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 2505 }: Central Line L(2, 2505) { 100, 190 }: Central Line L(100, 190) { 513, 676 }: Central Line L(513, 676) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_2505 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, SPIEKER CIRCLE} (0.5051, -0.1583) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.2449, 0.5665) X_2976 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, AC-INCIRCLE} (0.6020, 0.9165) A B C Ka Kb Kc X2 X2505 X100 X190 X513 X676 X2976 (a, b, c) = (5, 6, 7) | AB = 1

X2976 (RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, AC-INCIRCLE}) 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 \(f(a,b,c) = bc[(a - b)^{2}(a + c - b)^{2} - (a - c)^{2}(a + b - c)^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.590266463620\)
▸ Incident Central Lines3 lines

{2, 2505}, {100, 190}, {513, 676}

▸ Functional Relations1 relation

Notes

See X2975 for “AC-incircle.”