X2018

EXSIMILICENTER(GALLATLY CIRCLE, BEVAN CIRCLE)

X2018 is the exsimilicenter(gallatly circle, Bevan 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) { 39, 40 }: Central Line L(39, 40) { 1, 1689 }: Central Line L(1, 1689) { 165, 1690 }: Central Line L(165, 1690) { 9, 2013 }: Central Line L(9, 2013) { 57, 2008 }: Central Line L(57, 2008) { 371, 1700 }: Central Line L(371, 1700) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_40 = BEVAN POINT (0.4286, -0.0292) X_1 = INCENTER (0.5714, 0.2333) X_1689 = INVERSE-IN-BROCARD-CIRCLE OF X(1687) (0.6471, 0.3451) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_1690 = INVERSE-IN-BROCARD-CIRCLE OF X(1688) (0.5529, 0.1894) X_9 = MITTENPUNKT (0.5110, 0.1615) X_2013 = INSIMILICENTER(GALLATLY CIRCLE, SPIEKER CIRCLE) (0.5391, 0.1987) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.3669, 0.3221) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_1700 = INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5232, 0.1374) X_2018 = EXSIMILICENTER(GALLATLY CIRCLE, BEVAN CIRCLE) (0.6238, 0.3106) A B C X39 X40 X1 X1689 X165 X1690 X9 X2013 X57 X2008 X371 X1700 X2018 (a, b, c) = (5, 6, 7) | AB = 1

X2018 (EXSIMILICENTER(GALLATLY CIRCLE, BEVAN 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 \(f(A,B,C) = 1 + \cos A - \cos B - \cos C - 2 \sin(A + \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.357143459782\)
▸ Incident Central Lines21 lines

{1, 1689}, {9, 2013}, {10, 2544}, {39, 40}, {43, 2020}, {57, 2008}, {165, 1690}, {371, 1700}, {372, 1701}, {516, 2545}, {1670, 1703}, {1671, 1702}, {1695, 2019}, {1697, 2007}, {1698, 2009}, {1699, 2010}, {1704, 2011}, {1705, 2012}, {1706, 2014}, {2562, 2572}, {2563, 2573}