{"status": "success", "data": {"description_md": "The circular base of a hemisphere of radius $2$ rests on the base of a square pyramid of height $6$. The hemisphere is tangent to the other four faces of the pyramid. What is the edge-length of the base of the pyramid?\n\n$\\textbf{(A)}\\ 3\\sqrt{2} \\qquad<br>\\textbf{(B)}\\ \\frac{13}{3} \\qquad<br>\\textbf{(C)}\\ 4\\sqrt{2} \\qquad<br>\\textbf{(D)}\\ 6 \\qquad<br>\\textbf{(E)}\\ \\frac{13}{2}$\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>The circular base of a hemisphere of radius  <span class=\"katex--inline\">2</span>  rests on the base of a square pyramid of height  <span class=\"katex--inline\">6</span> . The hemisphere is tangent to the other four faces of the pyramid. What is the edge-length of the base of the pyramid?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 3\\sqrt{2} \\qquad\\textbf{(B)}\\ \\frac{13}{3} \\qquad\\textbf{(C)}\\ 4\\sqrt{2} \\qquad\\textbf{(D)}\\ 6 \\qquad\\textbf{(E)}\\ \\frac{13}{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": 3, "problem_name": "2011 AMC 12A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12A_p16", "prev": "/problem/11_amc12A_p14"}}