14. 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 $\frac{2 \pi R \sqrt{3}}{3}$
B $\frac{5 \pi R}{3}$
C $\frac{10 \pi R}{3}$
D $2 \pi R \sqrt{3}$
E $4 \pi R$
14. C By drawing radii and chords as shown, we can see that the triangles are equilateral and therefore each of the angles is $60^{\circ}$. Hence the left and right circles have each lost $120^{\circ}$ (one third) of their circumferences, and the central circle has one-third $\left(\frac{1}{6}+\frac{1}{6}\right)$ of its circumference remaining. Since $1-\frac{1}{3}+1-\frac{1}{3}+\frac{1}{3}=\frac{5}{3}$, the perimeter of the shape is $\frac{5}{3} \times 2 \pi R=\frac{10 \pi R}{3}$.