X1949

TRILINEAR POLE OF PU(19)

X1949 = cevapoint of X1950 and X1951
< 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) { 219, 296 }: Central Line L(219, 296) { 108, 1172 }: Central Line L(108, 1172) { 6, 1945 }: Central Line L(6, 1945) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1950 = CROSSSUM OF PU(20) (0.5478, 0.2410) X_1951 = CROSSDIFFERENCE OF PU(20) (3.2396, 6.6676) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_296 = ISOGONAL CONJUGATE OF X(243) (0.7214, -0.0918) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1945 = TRILINEAR POLE OF PU(18) (0.9520, -0.5335) X_1949 = TRILINEAR POLE OF PU(19) (0.7687, -0.1166) A B C X1950 X1951 X219 X296 X108 X1172 X6 X1945 X1949 (a, b, c) = (5, 6, 7) | AB = 1

X1949 (TRILINEAR POLE 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 \(f(a,b,c) = (\sin 2A)/(\cos^{2} A - \cos B \cos C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.847352433272\)
▸ Incident Central Lines3 lines

{6, 1945}, {108, 1172}, {219, 296}

▸ Functional Relations3 relations