X3151

X306-CEVA CONJUGATE OF X2

X3151 = reflection of X27 in X440
< 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) { 27, 440 }: Euler Line { 2, 3 }: Euler Line { 306, 1330 }: Central Line L(306, 1330) { 71, 1654 }: Central Line L(71, 1654) { 63, 2893 }: Central Line L(63, 2893) { 152, 2822 }: Central Line L(152, 2822) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_440 = COMPLEMENT OF X(27) (0.4970, 0.0943) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_1330 = ANTICOMPLEMENTARY CONJUGATE OF X(1) (0.3908, 0.0300) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_1654 = 1st HATZIPOLAKIS PARALLELIAN POINT (0.5055, 0.1656) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_2893 = ANTICOMPLEMENTARY CONJUGATE OF X(63) (0.4830, 0.1824) X_152 = REFLECTION OF X(20) IN X(101) (0.0408, 1.2414) X_2822 = ISOGONAL CONJUGATE OF X(2738) (0.4065, 0.7720) X_3151 = -CEVA CONJUGATE OF X(2) (0.3759, -0.2226) A B C X27 X440 X2 X3 X306 X1330 X71 X1654 X63 X2893 X152 X2822 X3151 (a, b, c) = (5, 6, 7) | AB = 1

X3151 (X306-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 \(x : y : z\) = X306 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): \(13.081758449845\)
▸ Incident Central Lines6 lines

{2, 3}, {63, 2893}, {71, 1654}, {144, 2895}, {152, 2822}, {306, 1330}

▸ Functional Relations5 relations

Notes

As a point on the Euler line, X3151 has Shinagawa coefficients \((E + \$bc\$, -2E - 2F - 2\$bc\$)\).