{"status": "success", "data": {"description_md": "In unit square $ABCD,$ the inscribed circle $\\omega$ intersects $\\overline{CD}$ at $M,$ and $\\overline{AM}$ intersects $\\omega$ at a point $P$ different from $M.$ What is $AP?$\n\n$\\textbf{(A) } \\frac{\\sqrt5}{12} \\qquad \\textbf{(B) } \\frac{\\sqrt5}{10} \\qquad \\textbf{(C) } \\frac{\\sqrt5}{9} \\qquad \\textbf{(D) } \\frac{\\sqrt5}{8} \\qquad \\textbf{(E) } \\frac{2\\sqrt5}{15}$\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>In unit square  <span class=\"katex--inline\">ABCD,</span>  the inscribed circle  <span class=\"katex--inline\">\\omega</span>  intersects  <span class=\"katex--inline\">\\overline{CD}</span>  at  <span class=\"katex--inline\">M,</span>  and  <span class=\"katex--inline\">\\overline{AM}</span>  intersects  <span class=\"katex--inline\">\\omega</span>  at a point  <span class=\"katex--inline\">P</span>  different from  <span class=\"katex--inline\">M.</span>  What is  <span class=\"katex--inline\">AP?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{\\sqrt5}{12} \\qquad \\textbf{(B) } \\frac{\\sqrt5}{10} \\qquad \\textbf{(C) } \\frac{\\sqrt5}{9} \\qquad \\textbf{(D) } \\frac{\\sqrt5}{8} \\qquad \\textbf{(E) } \\frac{2\\sqrt5}{15}</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": 2, "problem_name": "2020 AMC 12B Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12B_p11", "prev": "/problem/20_amc12B_p09"}}