UKMT Pink Kangaroo, 2019

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows a shape made of arcs of three circles, each with radius $R$ . The centres of the circles lie on the same straight line, and the middle circle passes through the centres of the other two circles. What is the perimeter of the shape?

(A) $\dfrac{2\pi R\sqrt{3}}{3}$ (B) $\dfrac{5\pi R}{3}$ (C) $\dfrac{10\pi R}{3}$ (D) $2\pi R\sqrt{3}$ (E) $4\pi R$

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