X755

EVEN (0, 4) CIRCUMCIRCLE POINT

X755 = isogonal conjugate of X754
< 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) { 39, 110 }: Central Line L(39, 110) { 99, 141 }: Central Line L(99, 141) { 76, 689 }: Central Line L(76, 689) { 6, 827 }: Central Line L(6, 827) { 733, 882 }: Central Line L(733, 882) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_754 = EVEN (0, 4) INFINITY POINT (0.1795, -0.2651) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_99 = STEINER POINT (0.1109, 0.4322) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_689 = TRILINEAR POLE OF LINE X(6)X(76) (0.0585, 0.3579) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_827 = o-(0, 4) CIRCUMCIRCLE POINT (0.3242, 0.5811) X_733 = EVEN (- 2, 2) CIRCUMCIRCLE POINT (1.0071, 0.0450) X_882 = ISOTOMIC CONJUGATE OF X(880) (0.9879, -0.0178) X_755 = EVEN (0, 4) CIRCUMCIRCLE POINT (0.9524, -0.1340) A B C X754 X39 X110 X99 X141 X76 X689 X6 X827 X733 X882 X755 (a, b, c) = (5, 6, 7) | AB = 1

X755 (EVEN (0, 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 \(f(a,b,c) = 1/[a ^{-1}(b^{4} + c^{4}) - a^{3}(b^{0} + c^{0})]\)
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): \(3.469059259665\)

X755 lies on the circumcircle.

▸ Incident Central Lines5 lines

{6, 827}, {39, 110}, {76, 689}, {99, 141}, {733, 882}

▸ Functional Relations4 relations