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$S$ is a point on the side $QR$ of a $\Delta PQR$ such that $\angle PSR = \angle QPR$. Prove that $PR^2 = QR \times SR$.
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Proving $\Delta PSR \sim \Delta QPR$ [By AA similarity criterion]
Hence, $\frac{SR}{PR} = \frac{PR}{QR} \implies PR^2 = QR \times SR$
Hence, $\frac{SR}{PR} = \frac{PR}{QR} \implies PR^2 = QR \times SR$