X743

EVEN (- 1, 2) CIRCUMCIRCLE POINT

X743 = isogonal conjugate of X742
< 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) { 2, 789 }: Central Line L(2, 789) { 31, 825 }: Central Line L(31, 825) { 101, 869 }: Central Line L(101, 869) { 665, 761 }: Central Line L(665, 761) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_742 = EVEN (- 1, 2) INFINITY POINT (0.1179, -0.2104) X_2 = CENTROID (0.5374, 0.2000) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_825 = o-(0, 3) CIRCUMCIRCLE POINT (0.2886, 0.5665) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_869 = INTERSECTION OF LINES X(1)X(2) AND X(31)X(32) (0.6039, 0.2651) X_665 = CROSSDIFFERENCE OF X(2) AND X(11) (1.4579, 1.0988) X_761 = EVEN (1, 4) CIRCUMCIRCLE POINT (0.9239, -0.1820) X_743 = EVEN (- 1, 2) CIRCUMCIRCLE POINT (1.0002, 0.0008) A B C X742 X2 X789 X31 X825 X101 X869 X665 X761 X743 (a, b, c) = (5, 6, 7) | AB = 1

X743 (EVEN (- 1, 2) 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 \(f(a,b,c) = 1/[a ^{-2}(b^{2} + c^{2}) - a^{1}(b ^{-1} + c ^{-1})]\)
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): \(0.351334943710\)

X743 lies on the circumcircle.

▸ Incident Central Lines4 lines

{2, 789}, {31, 825}, {101, 869}, {665, 761}

▸ Functional Relations4 relations