X150

REFLECTION OF X20 IN X103

X150 is the reflection of X20 in X103.
< 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, 103 }: Central Line L(20, 103) { 7, 80 }: Central Line L(7, 80) { 2, 101 }: Central Line L(2, 101) { 1, 147 }: Central Line L(1, 147) { 4, 152 }: Central Line L(4, 152) 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_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_7 = GERGONNE POINT (0.5903, 0.2769) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_2 = CENTROID (0.5374, 0.2000) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_1 = INCENTER (0.5714, 0.2333) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_4 = ORTHOCENTER (0.6122, 0.3958) X_152 = REFLECTION OF X(20) IN X(101) (0.0408, 1.2414) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) A B C X20 X103 X7 X80 X2 X101 X1 X147 X4 X152 X150 (a, b, c) = (5, 6, 7) | AB = 1

X150 (REFLECTION OF X20 IN X103) 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 \(f(a,b,c) = bc[b^{4} + c^{4} - a^{4} + a(bc^{2} +cb^{2} - b^{3} - c^{3}) - bc(a^{2} + b^{2} + c^{2}) + (b + c)a^{3}]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = b^{4} + c^{4} - a^{4} + a(bc^{2} +cb^{2} - b^{3} - c^{3}) - bc(a^{2} + b^{2} + c^{2}) + (b + c)a^{3}\)
Search Value (6, 9, 13): \(5.247092904763\)

X150 lies on the anticomplementary circle.

▸ Incident Central Lines10 lines

{1, 147}, {2, 101}, {4, 152}, {7, 80}, {20, 103}, {69, 668}, {85, 355}, {295, 334}, {348, 944}, {664, 952}

▸ Functional Relations7 relations