X152

REFLECTION OF X20 IN X101

X152 is the reflection of X20 in X101.
< 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) { 20, 101 }: Central Line L(20, 101) { 2, 103 }: Central Line L(2, 103) { 4, 150 }: Central Line L(4, 150) { 151, 928 }: Central Line L(151, 928) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_2 = CENTROID (0.5374, 0.2000) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_4 = ORTHOCENTER (0.6122, 0.3958) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) X_151 = REFLECTION OF X(20) IN X(109) (0.3395, 1.3793) X_928 = CROSSDIFFERENCE OF X(6) AND X(11) (1.0703, 0.4459) X_152 = REFLECTION OF X(20) IN X(101) (0.0408, 1.2414) A B C X20 X101 X2 X103 X4 X150 X151 X928 X152 (a, b, c) = (5, 6, 7) | AB = 1

X152 (REFLECTION OF X20 IN X101) 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 \(f(a,b,c) = (by + cz - ax)/a\), where \(x : y : z\) = X103
Barycentrics: \(a^{8} - a^{7} (b + c) + a^{6} (2 b^{2} + b c + 2 c^{2}) - a^{5} (5 b^{3} - b^{2} c - b c^{2} + 5 c^{3}) - a^{4} b c (b^{2} - 6 b c + c^{2}) + a^{3} (5 b^{5} + b^{4} c - 6 b^{3} c^{2} - 6 b^{2} c^{3} + b c^{4} + 5 c^{5}) - a^{2} (2 b^{6} + b^{5} c + 2 b^{4} c^{2} - 10 b^{3} c^{3} + 2 b^{2} c^{4} + b c^{5} + 2 c^{6}) + a (b^{7} - b^{6} c - 3 b^{5} c^{2} + 3 b^{4} c^{3} + 3 b^{3} c^{4} - 3 b^{2} c^{5} - b c^{6} + c^{7}) - b^{8} + b^{7} c + 2 b^{6} c^{2} - b^{5} c^{3} - 2 b^{4} c^{4} - b^{3} c^{5} + 2 b^{2} c^{6} + b c^{7} - c^{8} : :\)
Search Value (6, 9, 13): \(-16.600331726616\)

X152 lies on the anticomplementary circle.

▸ Incident Central Lines4 lines

{2, 103}, {4, 150}, {20, 101}, {151, 928}

▸ Functional Relations4 relations