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In the given figure, OA . OB = OC . OD. Show that $\angle A = \angle C$ and $\angle B = \angle D$.
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Given OA.OB = OC.OD
$\frac{OA}{OC} = \frac{OD}{OB}$
$\& \angle AOD = \angle COB$
$\therefore \triangle AOD \sim \triangle COB$
So, $\angle D = \angle B$ and $\angle A = \angle C$
$\frac{OA}{OC} = \frac{OD}{OB}$
$\& \angle AOD = \angle COB$
$\therefore \triangle AOD \sim \triangle COB$
So, $\angle D = \angle B$ and $\angle A = \angle C$