X3565

2nd MOSES CIRCUMCIRCLE POINT

X3565 = reflection of X3563 in X3
< 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) { 3563, 3 }: Central Line L(3563, 3) { 20, 98 }: Central Line L(20, 98) { 22, 111 }: Central Line L(22, 111) { 376, 1300 }: Central Line L(376, 1300) { 378, 1299 }: Central Line L(378, 1299) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3563 = 1st MOSES CIRCUMCIRCLE POINT (0.9328, 0.3724) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_98 = TARRY POINT (0.8891, -0.2281) X_22 = EXETER POINT (0.4143, -0.1221) X_111 = PARRY POINT (0.9885, -0.0457) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_1300 = COLLINGS TRANSFORM OF X(136) (0.9926, 0.2353) X_378 = REFLECTION OF X(22) IN X(3) (0.5857, 0.3262) X_1299 = COLLINGS TRANSFORM OF X(135) (0.7905, 0.5216) X_3565 = 2nd MOSES CIRCUMCIRCLE POINT (0.0672, -0.1683) A B C X3563 X3 X20 X98 X22 X111 X376 X1300 X378 X1299 X3565 (a, b, c) = (5, 6, 7) | AB = 1

X3565 (2nd MOSES CIRCUMCIRCLE POINT) 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 \(f(a,b,c) = a/[(3a^{2} - b^{2} - c^{2})(b^{2} - c^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.449291279142\)

X3565 lies on the circumcircle.

▸ Incident Central Lines10 lines

{2, 2374}, {3, 2971}, {20, 98}, {22, 111}, {376, 1300}, {378, 1299}, {842, 2071}, {858, 2770}, {1370, 2373}, {2456, 2698}

▸ Functional Relations8 relations

Notes

Let La be the reflection of the line X5X6 in line BC, and define Lb and Lc cyclically. Let A' = Lc∩Lc, B' = Lc∩La, C' = La∩Lb. The lines AA', BB', CC' concur in X3565. (Randy Hutson, January 29, 2018)