X1365

BRISSE TRANSFORM OF X110

X1365 = crosssum of X643 and X1098
< 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) { 56, 759 }: Central Line L(56, 759) { 125, 1109 }: Central Line L(125, 1109) { 1086, 1357 }: Central Line L(1086, 1357) { 1283, 1284 }: Central Line L(1283, 1284) { 7, 1366 }: Central Line L(7, 1366) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_759 = EVEN (1, 3) CIRCUMCIRCLE POINT (0.9498, -0.1389) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_1109 = TRILINEAR SQUARE OF X(523) (0.7246, 0.0705) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_1357 = BRISSE TRANSFORM OF X(100) (0.8000, 0.1866) X_1283 = 7th SHARYGIN POINT (0.7481, 0.0125) X_1284 = 8th SHARYGIN POINT (0.9846, 0.9156) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1366 = BRISSE TRANSFORM OF X(111) (0.4238, 0.4139) X_1365 = BRISSE TRANSFORM OF X(110) (0.7771, 0.1231) A B C X56 X759 X125 X1109 X1086 X1357 X1283 X1284 X7 X1366 X1365 (a, b, c) = (5, 6, 7) | AB = 1

X1365 (BRISSE TRANSFORM OF X110) 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) is as above X1354, using X = X110
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.169180953847\)

X1365 lies on the incircle.

▸ Incident Central Lines5 lines

{7, 1366}, {56, 759}, {125, 1109}, {1086, 1357}, {1283, 1284}

▸ Functional Relations6 relations