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UKMT Intermediate Mathematical Challenge, 2020

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows four semicircles, one with radius $2$ cm, touching the other three, which have radius $1$ cm. What is the total area, in cm $^2$ , of the shaded regions?

(A) $1$ (B) $\pi - 2$ (C) $2\pi - 5$ (D) $\dfrac{3}{2}$ (E) $\dfrac{1}{2}\pi$

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