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UKMT Intermediate Mathematical Challenge, 2024

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

A circle is inscribed in a semicircle with centre $O$ and diameter $AB$ . The centre of the circle is the point $P$ , where $PA = PO$ . What is the ratio of the radius of the circle to the radius of the semicircle?

(A) $4:9$ (B) $3:8$ (C) $3:7$ (D) $2:5$ (E) $1:2$

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