Let ABCC1B1A1 be a convex hexagon such that AB=BC, and suppose that the line segments AA1,BB1, and CC1 have the same perpendicular bisector. Let the diagonals AC1 and A1C meet at D, and denote by ω the circle ABC. Let ω intersect the circle A1BC1 again at E=B. Prove that the lines BB1 and DE intersect on ω. geometryperpendicular bisectorIMO Shortlist