AMC 12 2007b Problem 22

Two particles move along the edges of equilateral $\triangle ABC$ in the direction $$A\Rightarrow B\Rightarrow C\Rightarrow A,$$ starting simultaneously and moving at the same speed. One starts at $A$, and the other starts at the midpoint of $\overline{BC}$. The midpoint of the line segment joining the two particles traces out a path that encloses a region $R$. What is the ratio of the area of $R$ to the area of $\triangle ABC$?

$\mathrm {(A)} \frac{1}{16} \mathrm {(B)} \frac{1}{12} \mathrm {(C)} \frac{1}{9} \mathrm {(D)} \frac{1}{6} \mathrm {(E)} \frac{1}{4}$