X697

EVEN (- 4, - 3) CIRCUMCIRCLE POINT

1/[\(a^{m-1}(b^{n} + c^{n})\) - \(a^{n-1}(b^{m} + c^{m})\)],

hence the name “(m, n)-circumcircle point”.

< 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) { 100, 560 }: Central Line L(100, 560) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_696 = EVEN (- 4, - 3) INFINITY POINT (0.0157, -0.0688) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_560 = 4th POWER POINT (0.6520, 0.3639) X_697 = EVEN (- 4, - 3) CIRCUMCIRCLE POINT (0.9705, 0.2996) A B C X696 X100 X560 X697 (a, b, c) = (5, 6, 7) | AB = 1

X697 (EVEN (- 4, - 3) 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 \(f(a,b,c) = 1/[a ^{-5}(b ^{-3} + c ^{-3}) - a ^{-4}(b ^{-4} + c ^{-4})]\)
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): \(-0.534181898858\)

X697 lies on the circumcircle. This is one of several points of the form given by first trilinear

▸ Incident Central Lines1 line

{100, 560}

▸ Functional Relations2 relations