X699

EVEN (- 4, - 2) CIRCUMCIRCLE POINT

X699 = X385-cross conjugate of X251
< 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) { 32, 99 }: Central Line L(32, 99) { 251, 689 }: Central Line L(251, 689) { 172, 932 }: Central Line L(172, 932) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_698 = EVEN (- 4, - 2) INFINITY POINT (1.0503, 0.4852) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_99 = STEINER POINT (0.1109, 0.4322) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_689 = TRILINEAR POLE OF LINE X(6)X(76) (0.0585, 0.3579) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_932 = -CROSS CONJUGATE OF X(100) (0.0354, 0.3132) X_699 = EVEN (- 4, - 2) CIRCUMCIRCLE POINT (0.9822, 0.2692) A B C X698 X32 X99 X251 X689 X172 X932 X699 (a, b, c) = (5, 6, 7) | AB = 1

X699 (EVEN (- 4, - 2) 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 \(f(a,b,c) = 1/[a ^{-5}(b ^{-2} + c ^{-2}) - a ^{-3}(b ^{-4} + c ^{-4})]\)
Barycentrics: \(a^{2}/(a^{2} b^{4} + a^{2} c^{4} - b^{4} c^{2} - b^{2} c^{4}) : :\)
Search Value (6, 9, 13): \(-0.588121284539\)

X699 lies on the circumcircle.

▸ Incident Central Lines3 lines

{32, 99}, {172, 932}, {251, 689}

▸ Functional Relations6 relations