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(a) Prove that diagonals of a trapezium divide each other proportionally.
OR
(b) $S$ is a point on the side $QR$ of a $\Delta PQR$ such that $\angle PSR = \angle QPR$. Prove that $PR^2 = QR \times SR$.
OR
(b) $S$ 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 $\Delta AOB \sim \Delta COD$ [By AA similarity criterion]
$\therefore \frac{AO}{CO} = \frac{OB}{OD}$
OR
Proving $\Delta PSR \sim \Delta QPR$ [By AA similarity criterion]
Hence, $\frac{SR}{PR} = \frac{PR}{QR} \implies PR^2 = QR \times SR$
$\therefore \frac{AO}{CO} = \frac{OB}{OD}$
OR
Proving $\Delta PSR \sim \Delta QPR$ [By AA similarity criterion]
Hence, $\frac{SR}{PR} = \frac{PR}{QR} \implies PR^2 = QR \times SR$