X3251

INTERSECTION OF X1X_513 AND X42X_663

X3251 = reflection of X1635 in X1960
< 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) { 1635, 1960 }: Central Line L(1635, 1960) { 1, 513 }: Central Line L(1, 513) { 42, 663 }: Central Line L(42, 663) { 55, 667 }: Central Line L(55, 667) { 678, 1635 }: Central Line L(678, 1635) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1635 = TRIPOLAR CENTROID OF X(1) (2.1429, 2.0996) X_1960 = BICENTRIC SUM OF PU(25) (1.2500, 1.2247) X_1 = INCENTER (0.5714, 0.2333) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_678 = CROSSPOINT OF X(1) AND X(44) (0.3571, 0.3499) X_3251 = INTERSECTION OF X(1)X(513) AND X(42)X(663) (0.3571, 0.3499) A B C X1635 X1960 X1 X513 X42 X663 X55 X667 X678 X3251 (a, b, c) = (5, 6, 7) | AB = 1

X3251 (INTERSECTION OF X1X_513 AND X42X_663) 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 \(f(a,b,c) = (b - c)(2a - b - c)^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.683029380091\)
▸ Incident Central Lines5 lines

{1, 513}, {42, 663}, {55, 667}, {678, 1635}, {926, 1642}

▸ Functional Relations6 relations