2015 AMC 12B Problem 24

Four circles, no two of which are congruent, have centers at A, B, C, and D, and points P and Q lie on all four circles. The radius of circle A is \tfrac{5}{8} times the radius of circle B, and the radius of circle C is \tfrac{5}{8} times the radius of circle D. Furthermore, AB = CD = 39 and PQ = 48. Let R be the midpoint of \overline{PQ}. What is AR+BR+CR+DR ?

\textbf{(A)}\; 180 \qquad\textbf{(B)}\; 184 \qquad\textbf{(C)}\; 188 \qquad\textbf{(D)}\; 192\qquad\textbf{(E)}\; 196

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