X2452

REFLECTION OF X1316 IN X6

X2452 is the reflection of X1316 in X6.
< 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) { 1316, 6 }: Central Line L(1316, 6) { 6, 523 }: Central Line L(6, 523) { 98, 648 }: Central Line L(98, 648) { 30, 1351 }: Central Line L(30, 1351) { 3, 2407 }: Central Line L(3, 2407) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1316 = 5th MOSES INTERSECTION (0.5678, 0.2795) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_98 = TARRY POINT (0.8891, -0.2281) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_1351 = REFLECTION OF X(3) IN X(6) (0.7000, 0.4324) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2407 = GIBERT-SIMSON TRANSFORM OF X(110) (1.2056, 0.9180) X_2452 = REFLECTION OF X(1316) IN X(6) (0.6322, 0.2549) A B C X1316 X6 X523 X98 X648 X30 X1351 X3 X2407 X2452 (a, b, c) = (5, 6, 7) | AB = 1

X2452 (REFLECTION OF X1316 IN X6) 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 \(f(a,b,c) = bc[a^{8} - b^{2}c^{2}(b^{2} - c^{2})^{2} - a^{6}(b^{2} + c^{2}) + 2a^{2}(b^{2} - c^{2})^{2}(b^{2} + c^{2}) + a^{4}(5b^{2}c^{2} - 2b^{4} - 2c^{4})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.310297027365\)
▸ Incident Central Lines4 lines

{3, 2407}, {6, 523}, {30, 1351}, {98, 648}

▸ Functional Relations1 relation