X767

EVEN (3, 4) CIRCUMCIRCLE POINT

X767 = trilinear pole of line X6X693
< 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) { 75, 101 }: Central Line L(75, 101) { 76, 100 }: Central Line L(76, 100) { 85, 109 }: Central Line L(85, 109) { 110, 274 }: Central Line L(110, 274) { 112, 286 }: Central Line L(112, 286) { 108, 331 }: Central Line L(108, 331) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_766 = EVEN (3, 4) INFINITY POINT (0.2628, -0.3187) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_286 = -CROSS CONJUGATE OF X(27) (0.6033, 0.3810) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_331 = ISOTOMIC CONJUGATE OF X(219) (0.6062, 0.4046) X_767 = EVEN (3, 4) CIRCUMCIRCLE POINT (0.8487, -0.2706) A B C X766 X75 X101 X76 X100 X85 X109 X110 X274 X112 X286 X108 X331 X767 (a, b, c) = (5, 6, 7) | AB = 1

X767 (EVEN (3, 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 \(f(a,b,c) = 1/[a^{2}(b^{4} + c^{4}) - a^{3}(b^{3} + c^{3})]\)
Search Value (6, 9, 13): \(12.979818853253\)

X767 lies on the circumcircle.

▸ Incident Central Lines8 lines

{75, 101}, {76, 100}, {85, 109}, {108, 331}, {110, 274}, {112, 286}, {334, 813}, {825, 870}

▸ Functional Relations4 relations