X2499

RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, APOLLONIUS CIRCLE}

< 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) { 512, 650 }: Central Line L(512, 650) { 513, 676 }: Central Line L(513, 676) { 661, 926 }: Central Line L(661, 926) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) 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_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_926 = CROSSDIFFERENCE OF X(6) AND X(7) (0.0512, -0.1286) X_2499 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, APOLLONIUS CIRCLE} (46.7714, -24.2150) A B C X512 X650 X513 X676 X661 X926 X2499 (a, b, c) = (5, 6, 7) | AB = 1

X2499 (RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, APOLLONIUS 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 \(f(a,b,c) = a(b - c)[(b + c)(a^{2} + b^{2} + c^{2} - 4bc) - 2a(b^{2} + bc + c^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-40.490353126823\)
▸ Incident Central Lines3 lines

{512, 650}, {513, 676}, {661, 926}