X447

X2-HIRST INVERSE OF X27

X447 is the X2-hirst inverse of X27.
< 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 { 340, 540 }: Central Line L(340, 540) { 350, 811 }: Central Line L(350, 811) { 519, 648 }: Central Line L(519, 648) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_340 = ISOTOMIC CONJUGATE OF X(265) (1.2317, 1.4188) X_540 = DIRECTION OF VECTOR AX + BX + CX, where X = X(58) (0.9208, 0.6443) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_811 = ISOGONAL CONJUGATE OF X(810) (0.4151, 0.5616) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_447 = -HIRST INVERSE OF X(27) (0.8215, 0.9434) A B C X2 X3 X4 X340 X540 X350 X811 X519 X648 X447 (a, b, c) = (5, 6, 7) | AB = 1

X447 (X2-HIRST INVERSE OF X27) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(u^{2} - vw) : ca(v^{2} - wu) : ab(w^{2} - uv)\), where \(u : v : w\) = X28; e.g., \(u(a,b,c) = (\tan A)/(b + c)\)
Barycentrics: \(u^{2} - vw : v^{2} - wu : w^{2} - uv\)
Search Value (6, 9, 13): \(1.791080864593\)
▸ Incident Central Lines4 lines

{2, 3}, {340, 540}, {350, 811}, {519, 648}

▸ Functional Relations1 relation

Notes

As a point on the Euler line, X447 has Shinagawa coefficients \((2(E+F)^{3}FS^{2}-2\$abS_{C}\$(E+F)F +\$ab\$[4(E+F)^{2}-S^{2}]F, -(E+F)(2E-F)S^{2}-S^{4} + 2(\$abS_{C}\$S^{2}-\$ab\$(4E+F)S^{2})\).