{"status": "success", "data": {"description_md": "Let $ABCD$ be a cyclic quadrilateral. The side lengths of $ABCD$ are distinct integers less than $15$ such that $BC\\cdot CD=AB\\cdot DA$. What is the largest possible value of $BD$?\n\n$\\textbf{(A)}\\ \\sqrt{\\dfrac{325}{2}} \\qquad \\textbf{(B)}\\ \\sqrt{185} \\qquad \\textbf{(C)}\\ \\sqrt{\\dfrac{389}{2}} \\qquad \\textbf{(D)}\\ \\sqrt{\\dfrac{425}{2}} \\qquad \\textbf{(E)}\\ \\sqrt{\\dfrac{533}{2}}$\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>Let  <span class=\"katex--inline\">ABCD</span>  be a cyclic quadrilateral. The side lengths of  <span class=\"katex--inline\">ABCD</span>  are distinct integers less than  <span class=\"katex--inline\">15</span>  such that  <span class=\"katex--inline\">BC\\cdot CD=AB\\cdot DA</span> . What is the largest possible value of  <span class=\"katex--inline\">BD</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\sqrt{\\dfrac{325}{2}} \\qquad \\textbf{(B)}\\ \\sqrt{185} \\qquad \\textbf{(C)}\\ \\sqrt{\\dfrac{389}{2}} \\qquad \\textbf{(D)}\\ \\sqrt{\\dfrac{425}{2}} \\qquad \\textbf{(E)}\\ \\sqrt{\\dfrac{533}{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": 5, "problem_name": "2010 AMC 12B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12B_p23", "prev": "/problem/10_amc12B_p21"}}