Square A B C D has sides of length 4 , and M is the midpoint of \overline{C D}. A circle with radius 2 and center M intersects a circle with radius 4 and center A at points P and D. What is the distance from P to \overline{A D} ?
Answer Choices
A. 3
B. \dfrac{16}{5}
C. \dfrac{13}{4}
D. 2 \sqrt{3}
E. \dfrac{7}{2}