X839

o-(3, 4) CIRCUMCIRCLE POINT

X839 = trilinear pole of line X6X321
< 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) { 110, 668 }: Central Line L(110, 668) { 334, 741 }: Central Line L(334, 741) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_838 = ODD (3, 4) INFINITY POINT (1.0210, -0.1325) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_668 = TRILINEAR POLE OF LINE X(2)X(37) (0.0159, 0.3302) X_334 = ISOTOMIC CONJUGATE OF X(238) (1.0545, 0.0278) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_839 = o-(3, 4) CIRCUMCIRCLE POINT (0.0754, 0.3851) A B C X838 X110 X668 X334 X741 X839 (a, b, c) = (5, 6, 7) | AB = 1

X839 (o-(3, 4) CIRCUMCIRCLE POINT) 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 \(f(a,b,c) = 1/[a^{2}(b^{4} - c^{4}) + a^{3}(b^{3} - c^{3})]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(4.543806593145\)

X839 lies on the circumcircle.

▸ Incident Central Lines2 lines

{110, 668}, {334, 741}

▸ Functional Relations3 relations