2002 AMC 12A Problem 18

Let C_1 and C_2 be circles defined by (x-10)^2 + y^2 = 36 and (x+15)^2 + y^2 = 81 respectively. What is the length of the shortest line segment PQ that is tangent to C_1 at P and to C_2 at Q?

\text{(A) }15 \qquad \text{(B) }18 \qquad \text{(C) }20 \qquad \text{(D) }21 \qquad \text{(E) }24

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