In the given figure, $PA$ is a tangent to the circle drawn from the external point $P$ and $PBC$ is the secant to the circle with $BC$ as diameter. If $\angle AOC = 130°$, then find the measure of $\a

Question

In the given figure, $PA$ is a tangent to the circle drawn from the external point $P$ and $PBC$ is the secant to the circle with $BC$ as diameter. If $\angle AOC = 130°$, then find the measure of $\angle APB$, where $O$ is the centre of the circle.

Accepted Answer

Step 1: $\angle AOB = 180° - 130° = 50°$ (since $BOC$ is a diameter, $\angle AOB + \angle AOC = 180°$). $\angle OAP = 90°$ (radius $\perp$ tangent).
Step 2: $\angle APB = 180° - (50° + 90°) = 40°$.

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