X715

EVEN (- 3, - 1) CIRCUMCIRCLE POINT

X715 = isogonal conjugate of X714
< 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) { 31, 99 }: Central Line L(31, 99) { 110, 560 }: Central Line L(110, 560) { 82, 689 }: Central Line L(82, 689) { 81, 932 }: Central Line L(81, 932) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_714 = EVEN (- 3, - 1) INFINITY POINT (1.0302, 0.5186) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_99 = STEINER POINT (0.1109, 0.4322) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_560 = 4th POWER POINT (0.6520, 0.3639) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_689 = TRILINEAR POLE OF LINE X(6)X(76) (0.0585, 0.3579) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_932 = -CROSS CONJUGATE OF X(100) (0.0354, 0.3132) X_715 = EVEN (- 3, - 1) CIRCUMCIRCLE POINT (1.0000, 0.2040) A B C X714 X31 X99 X110 X560 X82 X689 X81 X932 X715 (a, b, c) = (5, 6, 7) | AB = 1

X715 (EVEN (- 3, - 1) 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 \(f(a,b,c) = 1/[a ^{-4}(b ^{-1} + c ^{-1}) - a ^{-2}(b ^{-3} + c ^{-3})]\)
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): \(-0.633860995106\)

X715 lies on the circumcircle.

▸ Incident Central Lines4 lines

{31, 99}, {81, 932}, {82, 689}, {110, 560}

▸ Functional Relations2 relations