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UKMT Hamilton Olympiad, 2020

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The diagram shows two semicircles with a common centre $O$ and a rectangle $OABC$ . The line through $O$ and $C$ meets the small semicircle at $D$ and the large semicircle at $E$ . The lengths $CD$ and $CE$ are equal.

What fraction of the large semicircle is shaded?

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