X1945

TRILINEAR POLE OF PU(18)

X1945 = X1952-Ceva conjugate of X296
< 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) { 109, 284 }: Central Line L(109, 284) { 19, 800 }: Central Line L(19, 800) { 333, 664 }: Central Line L(333, 664) { 37, 1569 }: Central Line L(37, 1569) { 673, 1465 }: Central Line L(673, 1465) { 6, 1949 }: Central Line L(6, 1949) 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_296 = ISOGONAL CONJUGATE OF X(243) (0.7214, -0.0918) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_19 = CLAWSON POINT (0.6246, 0.4244) X_800 = CROSSPOINT OF X(2) AND X(64) (0.6501, 0.3499) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_1569 = MOSES-CIRCLE ANTIPODE OF X(115) (0.4049, 0.3772) X_673 = TRILINEAR POLE OF LINE X(1)X(514) (0.9471, -0.0769) X_1465 = -BETH CONJUGATE OF X(908) (0.7719, 1.0314) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1949 = TRILINEAR POLE OF PU(19) (0.7687, -0.1166) X_1945 = TRILINEAR POLE OF PU(18) (0.9520, -0.5335) A B C X1952 X296 X109 X284 X19 X800 X333 X664 X37 X1569 X673 X1465 X6 X1949 X1945 (a, b, c) = (5, 6, 7) | AB = 1

X1945 (TRILINEAR POLE OF PU(18)) 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 \(f(a,b,c) = a/(\cos^{2} A - \cos B \cos C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.985948692800\)
▸ Incident Central Lines6 lines

{6, 1949}, {19, 800}, {37, 1569}, {109, 284}, {333, 664}, {673, 1465}

▸ Functional Relations2 relations