X688

CROSSDIFFERENCE OF X6 AND X76

As the isogonal conjugate of a point on the circumcircle, X688 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) { 30, 511 }: Central Line L(30, 511) { 6, 882 }: Central Line L(6, 882) { 669, 864 }: Central Line L(669, 864) { 798, 872 }: Central Line L(798, 872) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_689 = TRILINEAR POLE OF LINE X(6)X(76) (0.0585, 0.3579) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_882 = ISOTOMIC CONJUGATE OF X(880) (0.9879, -0.0178) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-4.3514, 4.6163) X_864 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(32) (0.7834, 0.8435) X_798 = CROSSDIFFERENCE OF X(1) AND X(75) (-13.4299, 10.5763) X_872 = INTERSECTION OF LINES X(37)X(42) AND X(43)X(75) (0.6029, 0.2656) X_688 = CROSSDIFFERENCE OF X(6) AND X(76) (1.0103, -0.1475) A B C X689 X30 X511 X6 X882 X669 X864 X798 X872 X688 (a, b, c) = (5, 6, 7) | AB = 1

X688 (CROSSDIFFERENCE OF X6 AND X76) 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 \(f(a,b,c) = a^{3}(b^{4} - c^{4})\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
▸ Incident Central Lines4 lines

{6, 882}, {30, 511}, {669, 864}, {798, 872}

▸ Functional Relations4 relations