IMO Shortlist 2015 problem G4

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Let ABC be an acute triangle and let M be the midpoint of AC. A circle \omega passing through B and M meets the sides AB and BC at points P and Q respectively. Let T be the point such that BPTQ is a parallelogram. Suppose that T lies on the circumcircle of ABC. Determine all possible values of \frac{BT}{BM}.