X1942

TRILINEAR POLE OF U(17)

X1942 = cevapoint of X450 and X1941
< 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) { 6, 1624 }: Central Line L(6, 1624) { 852, 895 }: Central Line L(852, 895) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_450 = -HIRST INVERSE OF X(4) (0.8978, 1.1430) X_1941 = CROSSSUM OF PU(17) (0.5282, 0.3794) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1624 = TCC-PERSPECTOR OF X(162) (0.4025, 0.6319) X_852 = -LINE CONJUGATE OF X(4) (0.3028, -0.4138) X_895 = ISOGONAL CONJUGATE OF X(468) (0.9484, -0.0134) X_1942 = TRILINEAR POLE OF U(17) (0.8014, -0.1046) A B C X450 X1941 X6 X1624 X852 X895 X1942 (a, b, c) = (5, 6, 7) | AB = 1

X1942 (TRILINEAR POLE OF U(17)) 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 \(f(a,b,c) = (\cos A)/(\cos^{4} A - \cos^{2} B \cos^{2} C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.350511909114\)
▸ Incident Central Lines2 lines

{6, 1624}, {852, 895}

▸ Functional Relations3 relations