In Fig. 1, $AB$ is diameter of a circle centered at $O$. $BC$ is tangent to the circle at $B$. If $OP$ bisects the chord $AD$ and $\angle AOP = 60°$, then find $m\angle C$.

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Question

In Fig. 1, $AB$ is diameter of a circle centered at $O$. $BC$ is tangent to the circle at $B$. If $OP$ bisects the chord $AD$ and $\angle AOP = 60°$, then find $m\angle C$.

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Accepted Answer

Step 1: $\because AP = PD \Rightarrow OP \perp AD$
Step 2: $	herefore \angle OAP = 30°$
Step 3: Also $\angle ABC = 90°$ (tangent $\perp$ radius)
Step 4: $\Rightarrow \angle C = 60°$

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