X761

EVEN (1, 4) CIRCUMCIRCLE POINT

X761 = isogonal conjugate of X760
< 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) { 665, 743 }: Central Line L(665, 743) { 1, 825 }: Central Line L(1, 825) { 76, 789 }: Central Line L(76, 789) { 101, 984 }: Central Line L(101, 984) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_760 = EVEN (1, 4) INFINITY POINT (0.2055, -0.2840) X_665 = CROSSDIFFERENCE OF X(2) AND X(11) (1.4579, 1.0988) X_743 = EVEN (- 1, 2) CIRCUMCIRCLE POINT (1.0002, 0.0008) X_1 = INCENTER (0.5714, 0.2333) X_825 = o-(0, 3) CIRCUMCIRCLE POINT (0.2886, 0.5665) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_761 = EVEN (1, 4) CIRCUMCIRCLE POINT (0.9239, -0.1820) A B C X760 X665 X743 X1 X825 X76 X789 X101 X984 X761 (a, b, c) = (5, 6, 7) | AB = 1

X761 (EVEN (1, 4) 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 \(f(a,b,c) = 1/[a^{0}(b^{4} + c^{4}) - a^{3}(b^{1} + c^{1})]\)
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): \(6.442789315879\)

X761 lies on the circumcircle.

▸ Incident Central Lines4 lines

{1, 825}, {76, 789}, {101, 984}, {665, 743}

▸ Functional Relations4 relations