{"status": "success", "data": {"description_md": "Circles $A, B,$ and $C$ each have radius 1. Circles $A$ and $B$ share one point of tangency. Circle $C$ has a point of tangency with the midpoint of $\\overline{AB}.$ What is the area inside circle $C$ but outside circle $A$ and circle $B?$\n\n$\\textbf{(A)}\\ 3 - \\frac{\\pi}{2} \\qquad<br>\\textbf{(B)}\\ \\frac{\\pi}{2} \\qquad<br>\\textbf{(C)}\\  2 \\qquad<br>\\textbf{(D)}\\ \\frac{3\\pi}{4} \\qquad<br>\\textbf{(E)}\\ 1+\\frac{\\pi}{2}$\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": "<p>Circles  <span class=\"katex--inline\">A, B,</span>  and  <span class=\"katex--inline\">C</span>  each have radius 1. Circles  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  share one point of tangency. Circle  <span class=\"katex--inline\">C</span>  has a point of tangency with the midpoint of  <span class=\"katex--inline\">\\overline{AB}.</span>  What is the area inside circle  <span class=\"katex--inline\">C</span>  but outside circle  <span class=\"katex--inline\">A</span>  and circle  <span class=\"katex--inline\">B?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 3 - \\frac{\\pi}{2} \\qquad\\textbf{(B)}\\ \\frac{\\pi}{2} \\qquad\\textbf{(C)}\\  2 \\qquad\\textbf{(D)}\\ \\frac{3\\pi}{4} \\qquad\\textbf{(E)}\\ 1+\\frac{\\pi}{2}</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2011 AMC 12A Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12A_p12", "prev": "/problem/11_amc12A_p10"}}