{"status": "success", "data": {"description_md": "[[Square]] $ABCD$ has side length $2$. A [[semicircle]] with [[diameter]] $\\overline{AB}$ is constructed inside the square, and the [[tangent (geometry)|tangent]] to the semicircle from $C$ intersects side $\\overline{AD}$ at $E$. What is the length of $\\overline{CE}$?\n\n<center>\n<img class=\"problem-image\" height=\"165\" src=\"https://latex.artofproblemsolving.com/d/a/e/daef6f3ebe3e1fc6cfacd8611db1d6d449c8d2d4.png\" width=\"168\"/>\n</center>\n\n$\\mathrm{(A) \\ } \\frac{2+\\sqrt{5}}{2} \\qquad \\mathrm{(B) \\ } \\sqrt{5} \\qquad \\mathrm{(C) \\ } \\sqrt{6} \\qquad \\mathrm{(D) \\ } \\frac{5}{2} \\qquad \\mathrm{(E) \\ } 5-\\sqrt{5}$", "description_html": "<p>[[Square]]  <span class=\"katex--inline\">ABCD</span>  has side length  <span class=\"katex--inline\">2</span> . A [[semicircle]] with [[diameter]]  <span class=\"katex--inline\">\\overline{AB}</span>  is constructed inside the square, and the [[tangent (geometry)|tangent]] to the semicircle from  <span class=\"katex--inline\">C</span>  intersects side  <span class=\"katex--inline\">\\overline{AD}</span>  at  <span class=\"katex--inline\">E</span> . What is the length of  <span class=\"katex--inline\">\\overline{CE}</span> ?</p>\n<center>\n<img class=\"problem-image\" height=\"165\" src=\"https://latex.artofproblemsolving.com/d/a/e/daef6f3ebe3e1fc6cfacd8611db1d6d449c8d2d4.png\" width=\"168\"/>\n</center>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{2+\\sqrt{5}}{2} \\qquad \\mathrm{(B) \\ } \\sqrt{5} \\qquad \\mathrm{(C) \\ } \\sqrt{6} \\qquad \\mathrm{(D) \\ } \\frac{5}{2} \\qquad \\mathrm{(E) \\ } 5-\\sqrt{5}</span> </p>\n<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": 4, "problem_name": "2004 AMC 10A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10A_p23", "prev": "/problem/04_amc10A_p21"}}