X2605

DIFFERENCE OF PU(71)

X2605 = midpoint of X663 and X1459
< 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) { 663, 1459 }: Central Line L(663, 1459) { 1, 523 }: Central Line L(1, 523) { 513, 663 }: Central Line L(513, 663) { 110, 1101 }: Central Line L(110, 1101) { 667, 834 }: Central Line L(667, 834) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_1459 = -BETH CONJUGATE OF X(521) (3.6667, -0.5443) X_1 = INCENTER (0.5714, 0.2333) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_1101 = TRILINEAR SQUARE OF X(110) (0.5344, 0.4306) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_834 = ODD (2, 3) INFINITY POINT (1.0367, -0.1085) X_2605 = DIFFERENCE OF PU(71) (6.1667, -1.9052) A B C X663 X1459 X1 X523 X513 X110 X1101 X667 X834 X2605 (a, b, c) = (5, 6, 7) | AB = 1

X2605 (DIFFERENCE OF PU(71)) 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 \(f(A,B,C) = \sin(C- A) - \sin(B - A)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-5.709103230921\)
▸ Incident Central Lines9 lines

{1, 523}, {11, 2616}, {110, 1101}, {512, 1326}, {513, 663}, {667, 834}, {1919, 2483}, {2245, 2609}, {2612, 2614}

▸ Functional Relations6 relations