2015 IMO shortlist

Let $M$ be the mid-point of $AC$ of an acute angled triangle $ABC$ . A circle $\xi$ passes through $B, M$ meets the sides $AB, BC$ again at $P, Q$ , respectively. Let $T$ be the point such that $BPTQ$ is a parallelogram. Suppose that $T$ lies on the circumcircle of $\triangle ABC$ .

Find the value of $\dfrac { BT }{ BM }$ .