X1947

CROSSSUM OF PU(19)

X1947 = X1952-Ceva conjugate of X1948
< 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) { 57, 264 }: Central Line L(57, 264) { 278, 330 }: Central Line L(278, 330) { 318, 377 }: Central Line L(318, 377) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1952 = TRILINEAR POLE OF PU(20) (0.7783, -0.2782) X_1948 = CROSSDIFFERENCE OF PU(19) (0.8752, 1.1631) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_330 = ISOTOMIC CONJUGATE OF X(192) (0.4364, 0.1391) X_318 = ISOTOMIC CONJUGATE OF X(77) (0.5514, 0.2839) X_377 = EULER LINE INTERCEPT OF LINE X(7)X(8) (0.5473, 0.2258) X_1947 = CROSSSUM OF PU(19) (0.5551, 0.3366) A B C X1952 X1948 X57 X264 X278 X330 X318 X377 X1947 (a, b, c) = (5, 6, 7) | AB = 1

X1947 (CROSSSUM OF PU(19)) 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 \(f(a,b,c) = (\cos^{2} A + \cos B \cos C) \csc 2A\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.119529047434\)
▸ Incident Central Lines3 lines

{57, 264}, {278, 330}, {318, 377}

▸ Functional Relations5 relations