{"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$\\mathrm{(A)}\\ \\left(2\\sqrt{3}+\\sqrt{5}\\right)\\pi\\qquad\\mathrm{(B)}\\ 6\\pi\\qquad\\mathrm{(C)}\\ \\left(3+\\sqrt{10}\\right)\\pi\\qquad\\mathrm{(D)}\\ \\left(\\sqrt{3}+2\\sqrt{5}\\right)\\pi\\qquad\\mathrm{(E)}\\ 2\\sqrt{10}\\pi$", "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>&#10;<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\\qquad\\mathrm{(E)}\\ 2\\sqrt{10}\\pi</span></p>&#10;", "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"}}