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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