IMO 2015 Shortlist G4
Let ABC be an acute triangle, and let M be the midpoint of AC. A circle ω passing through B and M meets the sides AB and...
Category: Geometry
Problem
Let ABC be an acute triangle, and let M be the midpoint of AC. A circle ω passing through B and M meets the sides AB and BC again at P and Q, respectively. Let T be the point such that the quadrilateral BPTQ is a parallelogram. Suppose that T lies on the circumcircle of the triangle ABC. Determine all possible values of BT{BM. (Russia)