2007 AMC 12B 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}\qquad \mathrm {(B)} \frac{1}{12}\qquad \mathrm {(C)} \frac{1}{9}\qquad \mathrm {(D)} \frac{1}{6}\qquad \mathrm {(E)} \frac{1}{4}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.