# Inspired by Clement V Durell

Geometry Level 3

The diagram below shows a circle with diameter $$AB$$, and $$P$$ lies on the straight line $$AB$$.

Given that $$QPR$$ is a chord such that $$\angle APQ = 45^\circ$$, find the value of $$\dfrac{AB^2}{PQ^2 + PR^2}$$.

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