Mathematics 0580 · IGCSE · Circle theorems II

Circle theorems II — practice question

For part (a), a circle with centre $O$ is drawn, and $A$, $B$ and $C$ are points on it. The angle $OBA$ is labelled $28^{\circ}$. For part (b), $P$, $Q$ and $R$ are points on a circle. $TU$ is a tangent to the circle at $P$. The angle $TPR$ is $47^{\circ}$ and the angle $PRQ$ is $52^{\circ}$. Both diagrams are marked NOT TO SCALE.
(a)[2]

Find the angle $ACB$.

(b)[2]

Find the angle $RPQ$.

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