X2020

EXSIMILICENTER(GALLATLY CIRCLE, APOLLONIUS CIRCLE)

X2020 is the exsimilicenter(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) { 2019, 2092 }: Brocard Axis { 3, 6 }: Brocard Axis { 10, 2009 }: Central Line L(10, 2009) { 43, 2018 }: Central Line L(43, 2018) { 181, 2008 }: Central Line L(181, 2008) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2019 = INSIMILICENTER(GALLATLY CIRCLE, APOLLONIUS CIRCLE) (0.5414, 0.1704) 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_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.5673, 0.2394) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_2018 = EXSIMILICENTER(GALLATLY CIRCLE, BEVAN CIRCLE) (0.6238, 0.3106) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.3669, 0.3221) X_2020 = EXSIMILICENTER(GALLATLY CIRCLE, APOLLONIUS CIRCLE) (0.6252, 0.3089) A B C X2019 X2092 X3 X6 X10 X2009 X43 X2018 X181 X2008 X2020 (a, b, c) = (5, 6, 7) | AB = 1

X2020 (EXSIMILICENTER(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): \(-0.305183291660\)
▸ Incident Central Lines6 lines

{3, 6}, {10, 2009}, {43, 2018}, {181, 2008}, {1682, 2007}, {1695, 2017}

▸ Functional Relations1 relation