X753

EVEN (0, 3) CIRCUMCIRCLE POINT

X753 = isogonal conjugate of X752
< 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, 825 }: Central Line L(6, 825) { 75, 789 }: Central Line L(75, 789) { 100, 984 }: Central Line L(100, 984) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_752 = EVEN (0, 3) INFINITY POINT (0.9166, 0.6478) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_825 = o-(0, 3) CIRCUMCIRCLE POINT (0.2886, 0.5665) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_753 = EVEN (0, 3) CIRCUMCIRCLE POINT (0.9725, -0.0907) A B C X752 X6 X825 X75 X789 X100 X984 X753 (a, b, c) = (5, 6, 7) | AB = 1

X753 (EVEN (0, 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 \(f(a,b,c) = 1/[a ^{-1}(b^{3} + c^{3}) - a^{2}(b^{0} + c^{0})]\)
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): \(2.265834391109\)

X753 lies on the circumcircle.

▸ Incident Central Lines3 lines

{6, 825}, {75, 789}, {100, 984}

▸ Functional Relations5 relations