X2019

INSIMILICENTER(GALLATLY CIRCLE, APOLLONIUS CIRCLE)

X2019 is the insimilicenter(gallatly circle, 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) { 2020, 2092 }: Brocard Axis { 3, 6 }: Brocard Axis { 10, 2010 }: Central Line L(10, 2010) { 43, 2017 }: Central Line L(43, 2017) { 181, 2007 }: Central Line L(181, 2007) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2020 = EXSIMILICENTER(GALLATLY CIRCLE, APOLLONIUS CIRCLE) (0.6252, 0.3089) X_2092 = DANNEELS-APOLLONIUS PERSPECTOR (0.5833, 0.2396) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.9341, -0.0718) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_2017 = INSIMILICENTER(GALLATLY CIRCLE, BEVAN CIRCLE) (0.5493, 0.1810) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.5746, 0.2319) X_2019 = INSIMILICENTER(GALLATLY CIRCLE, APOLLONIUS CIRCLE) (0.5414, 0.1704) A B C X2020 X2092 X3 X6 X10 X2010 X43 X2017 X181 X2007 X2019 (a, b, c) = (5, 6, 7) | AB = 1

X2019 (INSIMILICENTER(GALLATLY CIRCLE, 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 \(f(a,b,c) = (s^{2} - r^{2}) \cos A - 2rs \sin A + (s^{2} + r^{2}) \sin(A + \omega )\), where \(s = (a + b + c)/2\) and r = inradius = [area(ABC)]/s
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.159628951160\)
▸ Incident Central Lines6 lines

{3, 6}, {10, 2010}, {43, 2017}, {181, 2007}, {1682, 2008}, {1695, 2018}

▸ Functional Relations1 relation