Square ABCD has sides of length 4, and M is the midpoint of CD. A circle with radius 2 and center M intersects a circle with raidus 4 and center A at points P and D. What is the distance from P to AD?
[asy]unitsize(8mm);
defaultpen(linewidth(.8pt));
dotfactor=4;draw(Circle((2,0),2));
draw(Circle((0,4),4));
clip(scale(4)*unitsquare);
draw(scale(4)*unitsquare);
filldraw(Circle((2,0),0.07));
filldraw(Circle((3.2,1.6),0.07));
label("A",(0,4),NW);
label("B",(4,4),NE);
label("C",(4,0),SE);
label("D",(0,0),SW);
label("M",(2,0),S);
label("P",(3.2,1.6),N);[/asy]<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>516<spanclass=′latex−bold′>(C)</span>413<spanclass=′latex−bold′>(D)</span>23<spanclass=′latex−bold′>(E)</span>27