X717

EVEN (- 3, 0) CIRCUMCIRCLE POINT

X717 = isogonal conjugate of X716
< 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) { 6, 789 }: Central Line L(6, 789) { 560, 825 }: Central Line L(560, 825) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_716 = EVEN (- 3, 0) INFINITY POINT (1.0180, 0.5368) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_560 = 4th POWER POINT (0.6520, 0.3639) X_825 = o-(0, 3) CIRCUMCIRCLE POINT (0.2886, 0.5665) X_717 = EVEN (- 3, 0) CIRCUMCIRCLE POINT (1.0062, 0.1664) A B C X716 X6 X789 X560 X825 X717 (a, b, c) = (5, 6, 7) | AB = 1

X717 (EVEN (- 3, 0) 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 \(f(a,b,c) = 1/[a ^{-4}(b^{0} + c^{0}) - a ^{-1}(b ^{-3} + c ^{-3})]\)
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): \(-0.606970967575\)

X717 lies on the circumcircle.

▸ Incident Central Lines2 lines

{6, 789}, {560, 825}

▸ Functional Relations2 relations