X745

EVEN (- 1, 3) CIRCUMCIRCLE POINT

X745 = isogonal conjugate of X744
< 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) { 38, 99 }: Central Line L(38, 99) { 75, 689 }: Central Line L(75, 689) { 31, 827 }: Central Line L(31, 827) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_744 = EVEN (- 1, 3) INFINITY POINT (0.1365, -0.2286) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_99 = STEINER POINT (0.1109, 0.4322) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_689 = TRILINEAR POLE OF LINE X(6)X(76) (0.0585, 0.3579) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_827 = o-(0, 4) CIRCUMCIRCLE POINT (0.3242, 0.5811) X_745 = EVEN (- 1, 3) CIRCUMCIRCLE POINT (0.9892, -0.0432) A B C X744 X38 X99 X75 X689 X31 X827 X745 (a, b, c) = (5, 6, 7) | AB = 1

X745 (EVEN (- 1, 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 \(f(a,b,c) = 1/[a ^{-2}(b^{3} + c^{3}) - a^{2}(b ^{-1} + c ^{-1})]\)
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): \(0.961204679619\)

X745 lies on the circumcircle.

▸ Incident Central Lines3 lines

{31, 827}, {38, 99}, {75, 689}

▸ Functional Relations2 relations