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UKMT Senior Mathematical Challenge, 2021

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

A circle of radius $r$ and a right-angled isosceles triangle are drawn such that one of the shorter sides of the triangle is a diameter of the circle. What is the shaded area?

(A) $\sqrt{2}r$ (B) $r^2$ (C) $2\pi r$ (D) $\frac{\pi r^2}{4}$ (E) $(\sqrt{2} - 1)\pi r^2$

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