X2544

INSIMILICENTER(GALLATLY CIRCLE, (X4,2R))

The circle (X4,2R) is identified at X2474.
< 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) { 4, 39 }: Central Line L(4, 39) { 2, 1689 }: Central Line L(2, 1689) { 20, 1690 }: Central Line L(20, 1690) { 10, 2018 }: Central Line L(10, 2018) { 388, 2008 }: Central Line L(388, 2008) { 497, 2007 }: Central Line L(497, 2007) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_2 = CENTROID (0.5374, 0.2000) X_1689 = INVERSE-IN-BROCARD-CIRCLE OF X(1687) (0.6471, 0.3451) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_1690 = INVERSE-IN-BROCARD-CIRCLE OF X(1688) (0.5529, 0.1894) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_2018 = EXSIMILICENTER(GALLATLY CIRCLE, BEVAN CIRCLE) (0.6238, 0.3106) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.3669, 0.3221) X_497 = CROSSPOINT OF GERGONNE POINT AND NAGEL POINT (0.5593, 0.1851) X_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.5746, 0.2319) X_2544 = INSIMILICENTER(GALLATLY CIRCLE, (X(4),2R)) (0.5844, 0.2620) A B C X4 X39 X2 X1689 X20 X1690 X10 X2018 X388 X2008 X497 X2007 X2544 (a, b, c) = (5, 6, 7) | AB = 1

X2544 (INSIMILICENTER(GALLATLY CIRCLE, (X4,2R))) 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 \(f(A,B,C) = \cos B \cos C + \sin(A + \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.581332432683\)
▸ Incident Central Lines15 lines

{2, 1689}, {4, 39}, {10, 2018}, {20, 1690}, {371, 2547}, {372, 2546}, {388, 2008}, {497, 2007}, {516, 2017}, {1587, 1670}, {1588, 1671}, {2011, 2543}, {2012, 2542}, {2013, 2551}, {2014, 2550}