X3152

X307-CEVA CONJUGATE OF X2

X3152 = anticomplement of X29
< 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) { 2, 3 }: Euler Line { 40, 151 }: Central Line L(40, 151) { 145, 347 }: Central Line L(145, 347) { 78, 1330 }: Central Line L(78, 1330) { 307, 2893 }: Central Line L(307, 2893) { 2654, 3100 }: Central Line L(2654, 3100) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_40 = BEVAN POINT (0.4286, -0.0292) X_151 = REFLECTION OF X(20) IN X(109) (0.3395, 1.3793) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_1330 = ANTICOMPLEMENTARY CONJUGATE OF X(1) (0.3908, 0.0300) X_2893 = ANTICOMPLEMENTARY CONJUGATE OF X(63) (0.4830, 0.1824) X_2654 = SUM OF PU(82) (0.5822, 0.2761) X_3100 = INTERSECTION OF LINES X(1)X(7) AND X(2)X(33) (0.0000, -1.0887) X_3152 = -CEVA CONJUGATE OF X(2) (0.4316, -0.0769) A B C X307 X2 X3 X40 X151 X145 X347 X78 X1330 X2893 X2654 X3100 X3152 (a, b, c) = (5, 6, 7) | AB = 1

X3152 (X307-CEVA CONJUGATE OF X2) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X307 and \(u : v : w\) = X2
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(-2.668415961298\)
▸ Incident Central Lines7 lines

{2, 3}, {40, 151}, {78, 1330}, {145, 347}, {307, 2893}, {1654, 3177}, {2654, 3100}

▸ Functional Relations3 relations

Notes

As a point on the Euler line, X3152 has Shinagawa coefficients \(((E + F + \$bc\$)\$aS_{B}S_{C}\$ + (\$a\$F + \$(b+c)\$)S^{2}, 2\$a\$(E + F + \$bc\$)S^{2})\).