The diagram shows a circle $ABC$, with centre $O$. $AP$ and $BP$ are tangents to the circle.

Question

The diagram shows a circle $ABC$, with centre $O$. $AP$ and $BP$ are tangents to the circle. $\angle OAB = 25{}^\circ$ Stating your reasons clearly, find $\angle AOB$. $\angle PAB$. $\angle APB$. For this part, use a separate configuration with the same tangency relationships, without the $25^\circ$ condition from part (a). Given radius $5$ cm and $OP=16$ cm, find $AP$.

Accepted Answer

(a)(i) $130^\circ$ (a)(ii) $65^\circ$ (a)(iii) $50^\circ$ (b) $\sqrt{231}\text{ cm}\approx15.2\text{ cm}$ (3 s.f.)

Solving for Variables in Intersecting Circle Lines and Tangents

Solving for Variables in Intersecting Circle Lines and Tangents

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