IMO 2014 Shortlist G6
Let ABC be a fixed acute-angled triangle. Consider some points E and F lying on the sides AC and AB, respectively, and l...
Category: Geometry
Problem
Let ABC be a fixed acute-angled triangle. Consider some points E and F lying on the sides AC and AB, respectively, and let M be the midpoint of EF. Let the perpendicular bisector of EF intersect the line BC at K, and let the perpendicular bisector of MK intersect the lines AC and AB at S and T, respectively. We call the pair pE,Fq interesting, if the quadrilateral KSAT is cyclic. Suppose that the pairs pE1,F1q and pE2,F2q are interesting. Prove that E1E2 AB “ F1F2 AC . (Iran)