{"status": "success", "data": {"description_md": "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]
\n\n$\\textbf{(A)}\\ 3 \\qquad \\textbf{(B)}\\ \\frac {16}{5} \\qquad \\textbf{(C)}\\ \\frac {13}{4} \\qquad \\textbf{(D)}\\ 2\\sqrt {3} \\qquad \\textbf{(E)}\\ \\frac {7}{2}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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]

\\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}

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

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2003 AMC 12A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12A_p18", "prev": "/problem/03_amc12A_p16"}}