ISL 2015 G4

Last updated Sep 6, 2023 Edit Source

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 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 $\triangle ABC$. Determine all possible values of $\frac{BT}{BM}$.