Question 96
Let $\triangle ABC$ be an acute triangle, and let $M$ be the midpoint of the side $AC$. A circle through $B$ and $M$ meets the sides $AB$ and $BC$ again at $P$ and $Q$, respectively. The reflection $T$ of $B$ across the midpoint of the segment $PQ$ lies on the circle $ABC$. Evaluate the ratio $BT/BM$.