X3907

X512com[INVERSE(n(3rd EULER TRIANGLE))]

X3907 = crossdifference of every pair of points on line X6X893
< 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) { 1, 810 }: Central Line L(1, 810) { 1027, 1222 }: Central Line L(1027, 1222) { 1459, 2517 }: Central Line L(1459, 2517) { 663, 3716 }: Central Line L(663, 3716) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1 = INCENTER (0.5714, 0.2333) X_810 = CROSSPOINT OF X(1) AND X(163) (3.1222, -0.5010) X_1027 = INTERSECTION OF LINES X(1)X(514) AND X(6)X(513) (1.0130, 0.0424) X_1222 = ISOGONAL CONJUGATE OF X(1201) (0.5108, 0.1870) X_1459 = -BETH CONJUGATE OF X(521) (3.6667, -0.5443) X_2517 = RADICAL CENTER OF {CIRCUMCIRCLE, FUHRMANN CIRCLE, (X(4),2R)} (-14.6259, 4.7212) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_3716 = com(EXTOUCH TRIANGLE) (-0.4796, -0.6332) X_3907 = com[INVERSE(n(3rd EULER TRIANGLE))] (1.1014, 0.0376) A B C X30 X511 X1 X810 X1027 X1222 X1459 X2517 X663 X3716 X3907 (a, b, c) = (5, 6, 7) | AB = 1

X3907 (X512com[INVERSE(n(3rd EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b - c)(b + c - a)(a^{2} + bc)\)
▸ Linear Combinations1 combination
▸ Incident Central Lines5 lines

{1, 810}, {30, 511}, {663, 3716}, {1027, 1222}, {1459, 2517}

▸ Functional Relations1 relation

  • X3907 = crossdifference of every pair of points on line X6X893