X1952

TRILINEAR POLE OF PU(20)

X1952 = polar conjugate of X243
< 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) { 29, 65 }: Central Line L(29, 65) { 8, 201 }: Central Line L(8, 201) { 333, 664 }: Central Line L(333, 664) { 92, 1146 }: Central Line L(92, 1146) { 232, 1148 }: Central Line L(232, 1148) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1951 = CROSSDIFFERENCE OF PU(20) (3.2396, 6.6676) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_8 = NAGEL POINT (0.4694, 0.1333) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) 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_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_1146 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(8)}} (0.6866, 0.0428) X_232 = -CEVA CONJUGATE OF X(132) (0.6919, 0.7779) X_1148 = YIU-HATZIPOLAKIS POINT (0.4716, -1.3697) X_1952 = TRILINEAR POLE OF PU(20) (0.7783, -0.2782) A B C X1951 X29 X65 X8 X201 X333 X664 X92 X1146 X232 X1148 X1952 (a, b, c) = (5, 6, 7) | AB = 1

X1952 (TRILINEAR POLE OF PU(20)) 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 \(f(a,b,c) = bc/(\cos^{2} A - \cos B \cos C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-24.256040002446\)
▸ Incident Central Lines5 lines

{8, 201}, {29, 65}, {92, 1146}, {232, 1148}, {333, 664}

▸ Functional Relations5 relations