# 2015 IMO shortlist

Geometry Level pending

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 $$\dfrac { BT }{ BM }$$.

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