X2615

MIDPOINT OF PU(71)

X2615 is the midpoint of pu(71).
< 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) { 11, 115 }: Central Line L(11, 115) { 2610, 2611 }: Central Line L(2610, 2611) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_2610 = SUM OF PU(71) (2.7813, 1.7520) X_2611 = DIFFERENCE OF PU(71) (0.7448, 0.0628) X_2615 = MIDPOINT OF PU(71) (0.6849, 0.0131) A B C X11 X115 X2610 X2611 X2615 (a, b, c) = (5, 6, 7) | AB = 1

X2615 (MIDPOINT 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 \(f(A,B,C) = k(a,b,c) \csc(C - A) + h(a,b,c) \csc(B - A)\), where \(h(a,b,c) = a \csc(C - A) + b \csc(A - B) + c \csc(B - C)\), and \(k(a,b,c) = a \csc(B - A) + b \csc(C - B) + c \csc(A - C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(4.139377364258\)
▸ Incident Central Lines2 lines

{11, 115}, {2610, 2611}

▸ Functional Relations1 relation