X2539

EXSIMILICENTER(APOLLONIUS CIRCLE, SPIEKER RADICAL CIRCLE)

X2539 is the exsimilicenter(Apollonius circle, Spieker radical 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) { 5, 10 }: Central Line L(5, 10) { 181, 2535 }: Central Line L(181, 2535) { 386, 2537 }: Central Line L(386, 2537) { 573, 2536 }: Central Line L(573, 2536) { 1682, 2534 }: Central Line L(1682, 2534) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_2535 = EXSIMILICENTER(INCIRCLE, SPIEKER RADICAL CIRCLE) (0.5998, 0.2610) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_2537 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) (0.4272, -0.1877) X_573 = ORTHOHARMONIC OF X(58) (0.4583, 0.2009) X_2536 = INSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) (0.5089, 0.1377) X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) (0.5367, 0.1744) X_2534 = INSIMILICENTER(INCIRCLE, SPIEKER RADICAL CIRCLE) (0.5580, 0.2201) X_2539 = EXSIMILICENTER(APOLLONIUS CIRCLE, SPIEKER RADICAL CIRCLE) (0.6626, 0.4446) A B C X5 X10 X181 X2535 X386 X2537 X573 X2536 X1682 X2534 X2539 (a, b, c) = (5, 6, 7) | AB = 1

X2539 (EXSIMILICENTER(APOLLONIUS CIRCLE, SPIEKER RADICAL 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 \(f(a,b,c) = bc(b + c)r(r^{2} + s^{2})^{1/2} + a[4(\operatorname{area} ABC)^{2} + bc(r^{2} - s^{2}) \cos A]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.268816064497\)
▸ Incident Central Lines5 lines

{5, 10}, {181, 2535}, {386, 2537}, {573, 2536}, {1682, 2534}

Notes

See X2534.