X674

CROSSDIFFERENCE OF X6 AND X514

As the isogonal conjugate of a point on the circumcircle, X674 lies on the line at infinity.
< 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, 31 }: Central Line L(6, 31) { 51, 210 }: Central Line L(51, 210) { 30, 511 }: Central Line L(30, 511) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_675 = TRILINEAR POLE OF LINE X(6)X(514) (0.9212, -0.1860) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_674 = CROSSDIFFERENCE OF X(6) AND X(514) (0.2078, -0.2856) A B C X675 X6 X31 X51 X210 X30 X511 X674 (a, b, c) = (5, 6, 7) | AB = 1

X674 (CROSSDIFFERENCE OF X6 AND X514) 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 \(f(a,b,c) = a[b^{3} + c^{3} - a(b^{2} + c^{2})]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
▸ Incident Central Lines3 lines

{6, 31}, {30, 511}, {51, 210}

▸ Functional Relations2 relations