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UKMT Hamilton Olympiad, 2016

Geometry Difficulty 2.0 Junior Prove it United Kingdom

The diagram shows two arcs. Arc $AB$ is one eighth of a circle with centre $C$ , and arc $AC$ is one quarter of a circle with centre $D$ . The points $A$ and $B$ are joined by straight lines to $C$ , and $A$ and $C$ are joined by straight lines to $D$ . Prove that the area of the shaded triangle $T$ is equal to the area of the shaded region $R$ .

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