X2453

REFLECTION OF X6 IN X1316

X2453 is the reflection of X6 in X1316.
< 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) { 6, 1316 }: Central Line L(6, 1316) { 23, 183 }: Central Line L(23, 183) { 98, 338 }: Central Line L(98, 338) { 6, 523 }: Central Line L(6, 523) { 30, 599 }: Central Line L(30, 599) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1316 = 5th MOSES INTERSECTION (0.5678, 0.2795) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_98 = TARRY POINT (0.8891, -0.2281) X_338 = CEVAPOINT OF X(115) AND X(125) (0.6941, 0.0587) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_599 = ISOTOMIC CONJUGATE OF X(598) (0.4748, 0.1327) X_2453 = REFLECTION OF X(6) IN X(1316) (0.5356, 0.2918) A B C X6 X1316 X23 X183 X98 X338 X523 X30 X599 X2453 (a, b, c) = (5, 6, 7) | AB = 1

X2453 (REFLECTION OF X6 IN X1316) 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 \(f(a,b,c) = bc(a^{2} + b^{2} + c^{2})[a^{8} - a^{6}(b^{2} + c^{2}) + a^{4}(b^{4} - b^{2}c^{2} + c^{4}) + a^{2}(b^{4}c^{2} + b^{2}c^{4} - b^{6} - c^{6}) + 2b^{2}c^{2}(b^{2} - c^{2})^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.358131430467\)
▸ Incident Central Lines7 lines

{6, 523}, {23, 183}, {30, 599}, {98, 338}, {378, 477}, {476, 1995}, {691, 1003}

▸ Functional Relations2 relations