Problem
2003 AMC 12A Problem 17
Square ABCD has sides of length 4, and M is the midpoint of \overline{CD}. 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{AD}?
![[asy] pair A,B,C,D,M,P; D=(0,0); C=(10,0); B=(10,10); A=(0,10); M=(5,0); P=(8,4); dot(M); dot(P); draw(A--B--C--D--cycle,linewidth(0.7)); draw((5,5)..D--C..cycle,linewidth(0.7)); draw((7.07,2.93)..B--A--D..cycle,linewidth(0.7)); label("$A$",A,NW); label("$B$",B,NE); label("$C$",C,SE); label("$D$",D,SW); label("$M$",M,S); label("$P$",P,N); [/asy]](/static/aops/b1f5dc5a294bcfb2e9f16e90d2d7b6f5843d52e1.png)
\textbf{(A)}\ 3 \qquad \textbf{(B)}\ \frac {16}{5} \qquad \textbf{(C)}\ \frac {13}{4} \qquad \textbf{(D)}\ 2\sqrt {3} \qquad \textbf{(E)}\ \frac {7}{2}
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