17. The shaded region in the diagram, bounded by two concentric circles, is called an annulus. The circles have radii $2 \mathrm{~cm}$ and $14 \mathrm{~cm}$.
The dashed circle divides the area of this annulus into two equal areas. What is its radius?
A $9 \mathrm{~cm} \quad$ B $10 \mathrm{~cm} \quad$ C $11 \mathrm{~cm} \quad$ D $12 \mathrm{~cm} \quad$ E $13 \mathrm{~cm}$
17. B Let the radius of the dashed circle be $r \mathrm{~cm}$. Then one of the equal areas is bounded by circles of radii of $14 \mathrm{~cm}$ and $r \mathrm{~cm}$, whilst the other is bounded by circles of radii of $r \mathrm{~cm}$ and $2 \mathrm{~cm}$. So $\pi \times 14^{2}-\pi r^{2}=\pi r^{2}-\pi \times 2^{2}$. Dividing throughout by $\pi$ gives $196-r^{2}=r^{2}-4$. So $2 r^{2}=200$, that is $r^{2}=100$. Therefore $r=10$ (since $\left.r>0\right)$.