X2600

DIFFERENCE OF PU(69)

X2600 = crosssum of X1 and X2600
< 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) { 44, 513 }: Central Line L(44, 513) { 2599, 2604 }: Central Line L(2599, 2604) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_2599 = SUM OF PU(69) (0.5631, 0.2411) X_2604 = MIDPOINT OF PU(69) (0.5630, 0.2410) X_2600 = DIFFERENCE OF PU(69) (2.7368, 1.7763) A B C X44 X513 X2599 X2604 X2600 (a, b, c) = (5, 6, 7) | AB = 1

X2600 (DIFFERENCE OF PU(69)) 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 \(f(A,B,C) = \sec(C- A) - \sec(B - A)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-5.383992269761\)
▸ Incident Central Lines2 lines

{44, 513}, {2599, 2604}

▸ Functional Relations4 relations

Notes

X2600 is the perspector of triangle ABC and the tangential triangle of the hyperbola that passes through the points A, B, C, X1, and X5. (Randy Hutson, 9/23/2011)