{"status": "success", "data": {"description_md": "Consider all quadrilaterals $ABCD$ such that $AB=14$, $BC=9$, $CD=7$, and $DA=12$. What is the radius of the largest possible circle that fits inside or on the boundary of such a quadrilateral?\n\n$\\textbf{(A)}\\ \\sqrt{15} \\qquad<br>\\textbf{(B)}\\ \\sqrt{21} \\qquad<br>\\textbf{(C)}\\ 2\\sqrt{6} \\qquad<br>\\textbf{(D)}\\ 5 \\qquad<br>\\textbf{(E)}\\ 2\\sqrt{7}$\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>Consider all quadrilaterals  <span class=\"katex--inline\">ABCD</span>  such that  <span class=\"katex--inline\">AB=14</span> ,  <span class=\"katex--inline\">BC=9</span> ,  <span class=\"katex--inline\">CD=7</span> , and  <span class=\"katex--inline\">DA=12</span> . What is the radius of the largest possible circle that fits inside or on the boundary of such a quadrilateral?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\sqrt{15} \\qquad\\textbf{(B)}\\ \\sqrt{21} \\qquad\\textbf{(C)}\\ 2\\sqrt{6} \\qquad\\textbf{(D)}\\ 5 \\qquad\\textbf{(E)}\\ 2\\sqrt{7}</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": 5, "problem_name": "2011 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12A_p25", "prev": "/problem/11_amc12A_p23"}}