X719

EVEN (- 3, 1) CIRCUMCIRCLE POINT

X719 = isogonal conjugate of X718
< 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) { 1, 689 }: Central Line L(1, 689) { 560, 827 }: Central Line L(560, 827) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_718 = EVEN (- 3, 1) INFINITY POINT (0.0703, -0.1553) X_1 = INCENTER (0.5714, 0.2333) X_689 = TRILINEAR POLE OF LINE X(6)X(76) (0.0585, 0.3579) X_560 = 4th POWER POINT (0.6520, 0.3639) X_827 = o-(0, 4) CIRCUMCIRCLE POINT (0.3242, 0.5811) X_719 = EVEN (- 3, 1) CIRCUMCIRCLE POINT (1.0097, 0.1268) A B C X718 X1 X689 X560 X827 X719 (a, b, c) = (5, 6, 7) | AB = 1

X719 (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 \(f(a,b,c) = 1/[a ^{-4}(b^{1} + c^{1}) - a^{0}(b ^{-3} + c ^{-3})]\)
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): \(-0.513068928253\)

X719 lies on the circumcircle.

▸ Incident Central Lines2 lines

{1, 689}, {560, 827}

▸ Functional Relations2 relations