In the given figure, two tangents $TP$ and $TQ$ are drawn to a circle with centre $O$ from an external point $T$. Prove that $\angle PTQ = 2\angle OPQ$.

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Question

In the given figure, two tangents $TP$ and $TQ$ are drawn to a circle with centre $O$ from an external point $T$. Prove that $\angle PTQ = 2\angle OPQ$.

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Accepted Answer

Step 1: Let $\angle OPQ = 	heta$.
$	herefore \angle TPQ = \angle TOP = 90° - 	heta$
Step 2: In $	riangle TPQ$: $2(90° - 	heta) + \angle PTQ = 180°$
$	herefore \angle PTQ = 2	heta = 2\angle OPQ$

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