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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