X151

REFLECTION OF X20 IN X109

X151 is the reflection of X20 in X109.
< 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, 109 }: Central Line L(20, 109) { 2, 102 }: Central Line L(2, 102) { 49, 962 }: Central Line L(49, 962) { 152, 928 }: Central Line L(152, 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_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_2 = CENTROID (0.5374, 0.2000) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_962 = LONGUET-HIGGINS POINT (0.7551, 0.6582) X_152 = REFLECTION OF X(20) IN X(101) (0.0408, 1.2414) X_928 = CROSSDIFFERENCE OF X(6) AND X(11) (1.0703, 0.4459) X_151 = REFLECTION OF X(20) IN X(109) (0.3395, 1.3793) A B C X20 X109 X2 X102 X49 X962 X152 X928 X151 (a, b, c) = (5, 6, 7) | AB = 1

X151 (REFLECTION OF X20 IN X109) 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 \(x : y : z\) = X102
Barycentrics: \(a^{12} + a^{11} (b + c) + a^{10} b c + a^{9} (3 b^{3} - b^{2} c - b c^{2} + 3 c^{3}) - a^{8} (3 b^{4} + b^{3} c + b c^{3} + 3 c^{4}) - 2 a^{7} (7 b^{5} + b^{4} c - 4 b^{3} c^{2} - 4 b^{2} c^{3} + b c^{4} + 7 c^{5}) - 2 a^{6} b c (b^{4} - 2 b^{3} c - 6 b^{2} c^{2} - 2 b c^{3} + c^{4}) + 2 a^{5} (7 b^{7} + b^{6} c - 5 b^{5} c^{2} - 3 b^{4} c^{3} - 3 b^{3} c^{4} - 5 b^{2} c^{5} + b c^{6} + 7 c^{7}) + a^{4} (3 b^{8} + 2 b^{7} c - 4 b^{6} c^{2} - 2 b^{5} c^{3} + 2 b^{4} c^{4} - 2 b^{3} c^{5} - 4 b^{2} c^{6} + 2 b c^{7} + 3 c^{8}) - a^{3} (3 b^{9} - b^{8} c + 8 b^{6} c^{3} - 10 b^{5} c^{4} - 10 b^{4} c^{5} + 8 b^{3} c^{6} - b c^{8} + 3 c^{9}) + a^{2} b c (b^{8} - 4 b^{7} c - 12 b^{6} c^{2} + 4 b^{5} c^{3} + 22 b^{4} c^{4} + 4 b^{3} c^{5} - 12 b^{2} c^{6} - 4 b c^{7} + c^{8}) - a (b^{11} + b^{10} c - 3 b^{9} c^{2} - 3 b^{8} c^{3} + 2 b^{7} c^{4} + 2 b^{6} c^{5} + 2 b^{5} c^{6} + 2 b^{4} c^{7} - 3 b^{3} c^{8} - 3 b^{2} c^{9} + b c^{10} + c^{11}) - b^{12} - b^{11} c + 4 b^{10} c^{2} + 3 b^{9} c^{3} - 7 b^{8} c^{4} - 2 b^{7} c^{5} + 8 b^{6} c^{6} - 2 b^{5} c^{7} - 7 b^{4} c^{8} + 3 b^{3} c^{9} + 4 b^{2} c^{10} - b c^{11} - c^{12} : :\)
Search Value (6, 9, 13): \(-18.919492884960\)

X151 lies on the anticomplementary circle.

▸ Incident Central Lines4 lines

{2, 102}, {20, 109}, {49, 962}, {152, 928}

▸ Functional Relations3 relations