Let △ABC be a triangle with circumcircle τ. The tangentlines to τ through A and B intersect at T. The circle through A, B and T intersects BC and AC again at D and E, respectively; CT and BE intersect at F.
Suppose D is the midpoint of BC. Calculate the ratio BF:BE.(Swiss Mathematical Olympiad 2011, Final round, problem 5) ratiogeometrycircumcircleperpendicular bisectorgeometry proposed