Mathematics 0580 · IGCSE · Circle theorems I

Circle theorems I — practice question

A, B, P and Q are on a circle with centre $O$. The angle $APB$ is $56^{\circ}$. The diagram shows the circle with $A$, $B$, $P$ and $Q$ labelled. The angle at centre $O$ between $OA$ and $OB$ is marked $x^{\circ}$. The angle at $Q$ between $QA$ and $QB$ is marked $y^{\circ}$. Diagram not to scale.
(a)[1]

Find the numerical value of $x$.

(b)[1]

Find the numerical value of $y$.

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