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SMO 2025 Senior Round 1 Question 19

SMO · SMO 2025 Senior Round 1

Question 19

In the diagram below, a smaller circle has its centre $O$ on the circumference of a bigger circle. The smaller circle intersects the bigger circle at $P$ and $Q$. Chord $PR$ of the smaller circle is tangent to the bigger circle. Line $RO$ is extended to intersect the bigger circle at $S$. Given that $\angle PRS=20^\circ$ and $\angle SPQ=x^\circ$, find $x$.

Question illustration