{"status": "success", "data": {"description_md": "A triangle with sides of length $5, 12,$ and $13$ has both an inscribed and a circumscribed circle. What is the distance between the centers of those circles?\n\n$\\mathrm{(A) \\ } \\frac{3\\sqrt{5}}{2} \\qquad \\mathrm{(B) \\ } \\frac{7}{2} \\qquad \\mathrm{(C) \\ } \\sqrt{15} \\qquad \\mathrm{(D) \\ } \\frac{\\sqrt{65}}{2} \\qquad \\mathrm{(E) \\ } \\frac{9}{2}$", "description_html": "<p>A triangle with sides of length  <span class=\"katex--inline\">5, 12,</span>  and  <span class=\"katex--inline\">13</span>  has both an inscribed and a circumscribed circle. What is the distance between the centers of those circles?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{3\\sqrt{5}}{2} \\qquad \\mathrm{(B) \\ } \\frac{7}{2} \\qquad \\mathrm{(C) \\ } \\sqrt{15} \\qquad \\mathrm{(D) \\ } \\frac{\\sqrt{65}}{2} \\qquad \\mathrm{(E) \\ } \\frac{9}{2}</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 10B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10B_p23", "prev": "/problem/04_amc10B_p21"}}