Tangents $PA$ and $PB$ touch a circle with centre $O$ at $A$ and $B$. The line segment \(O

Question

Tangents $PA$ and $PB$ touch a circle with centre $O$ at $A$ and $B$. The line segment $OP$ is drawn, and $\angle APO=32^\circ$. The diagram is not drawn to scale. Prove that $OP$ bisects $\angle APB$, using congruent triangles. Do not assume that the two angles at $P$ are equal.[3] Find $\angle APB$ and the minor angle $AOB$, giving reasons.[2]

Accepted Answer

(a) $\triangle OAP\equiv\triangle OBP$ by RHS, so the two angles at $P$ are equal. (b) $\angle APB=64^\circ$, minor $\angle AOB=116^\circ$.

Bisecting the angle between two tangents

Bisecting the angle between two tangents

Solution:

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