{"status": "success", "data": {"description_md": "Rectangle $PQRS$ lies in a plane with $PQ=RS=2$ and $QR=SP=6$. The rectangle is rotated $90^\\circ$ clockwise about $R$, then rotated $90^\\circ$ clockwise about the point $S$ moved to after the first rotation. What is the length of the path traveled by point $P$?\n\n$\\mathrm{(A)}\\ \\left(2\\sqrt{3}+\\sqrt{5}\\right)\\pi\\qquad\\mathrm{(B)}\\ 6\\pi\\qquad\\mathrm{(C)}\\ \\left(3+\\sqrt{10}\\right)\\pi\\qquad\\mathrm{(D)}\\ \\left(\\sqrt{3}+2\\sqrt{5}\\right)\\pi\\\\\\mathrm{(E)}\\ 2\\sqrt{10}\\pi$", "description_html": "<p>Rectangle  <span class=\"katex--inline\">PQRS</span>  lies in a plane with  <span class=\"katex--inline\">PQ=RS=2</span>  and  <span class=\"katex--inline\">QR=SP=6</span> . The rectangle is rotated  <span class=\"katex--inline\">90^\\circ</span>  clockwise about  <span class=\"katex--inline\">R</span> , then rotated  <span class=\"katex--inline\">90^\\circ</span>  clockwise about the point  <span class=\"katex--inline\">S</span>  moved to after the first rotation. What is the length of the path traveled by point  <span class=\"katex--inline\">P</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\left(2\\sqrt{3}+\\sqrt{5}\\right)\\pi\\qquad\\mathrm{(B)}\\ 6\\pi\\qquad\\mathrm{(C)}\\ \\left(3+\\sqrt{10}\\right)\\pi\\qquad\\mathrm{(D)}\\ \\left(\\sqrt{3}+2\\sqrt{5}\\right)\\pi\\\\\\mathrm{(E)}\\ 2\\sqrt{10}\\pi</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": 3, "problem_name": "2008 AMC 10A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc10A_p20", "prev": "/problem/08_amc10A_p18"}}