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UKMT Senior Kangaroo, 2016

Geometry Difficulty 2.0 Junior Prove it United Kingdom

The diagram shows two concentric circles. Chord $AB$ of the larger circle is tangential to the smaller circle. The length of $AB$ is 32 cm and the area of the shaded region is $k\pi\,\text{cm}^2$ . What is the value of $k$ ?

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