X2535

EXSIMILICENTER(INCIRCLE, SPIEKER RADICAL CIRCLE)

X2535 is the exsimilicenter(incircle, 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) { 1, 2 }: Nagel Line { 11, 2541 }: Central Line L(11, 2541) { 12, 2540 }: Central Line L(12, 2540) { 55, 2536 }: Central Line L(55, 2536) { 56, 2537 }: Central Line L(56, 2537) { 181, 2539 }: Central Line L(181, 2539) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_2541 = EXSIMILICENTER(NINE-POINT CIRCLE, SPIEKER RADICAL CIRCLE) (0.5790, 0.2909) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_2540 = INSIMILICENTER(NINE-POINT CIRCLE, SPIEKER RADICAL CIRCLE) (0.5461, 0.2305) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_2536 = INSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) (0.5089, 0.1377) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_2537 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) (0.4272, -0.1877) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_2539 = EXSIMILICENTER(APOLLONIUS CIRCLE, SPIEKER RADICAL CIRCLE) (0.6626, 0.4446) X_2535 = EXSIMILICENTER(INCIRCLE, SPIEKER RADICAL CIRCLE) (0.5998, 0.2610) A B C X1 X2 X11 X2541 X12 X2540 X55 X2536 X56 X2537 X181 X2539 X2535 (a, b, c) = (5, 6, 7) | AB = 1

X2535 (EXSIMILICENTER(INCIRCLE, 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 \(f(a,b,c) = bc[(b + c)r - ad]\), where \(d = (r^{2} + s^{2})^{1/2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.246144671745\)
▸ Incident Central Lines7 lines

{1, 2}, {11, 2541}, {12, 2540}, {55, 2536}, {56, 2537}, {181, 2539}, {1682, 2538}

Notes

See X2534.