In the given figure, $OA \cdot OB = OC \cdot OD$. Show that $\angle A = \angle C$ and $\angle B = \angle D$.

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Question

In the given figure, $OA \cdot OB = OC \cdot OD$. Show that $\angle A = \angle C$ and $\angle B = \angle D$.

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Accepted Answer

Step 1: Given $OA \cdot OB = OC \cdot OD$
$\Rightarrow \frac{OA}{OC} = \frac{OD}{OB}$
$\angle AOD = \angle COB$ (vertically opposite angles)
Step 2: $	herefore 	riangle AOD \sim 	riangle COB$ (SAS similarity)
So, $\angle D = \angle B$ and $\angle A = \angle C$

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