{"status": "success", "data": {"description_md": "Square $ABCD$ has side length $1$. Points $P$, $Q$, $R$, and $S$ each lie on a side of $ABCD$ such that $APQCRS$ is an equilateral convex hexagon with side length $s$. What is $s$?\n\n$\\textbf{(A) } \\frac{\\sqrt{2}}{3} \\qquad \\textbf{(B) } \\frac{1}{2} \\qquad \\textbf{(C) } 2 - \\sqrt{2} \\qquad \\textbf{(D) } 1 - \\frac{\\sqrt{2}}{4} \\qquad \\textbf{(E) } \\frac{2}{3}$", "description_html": "<p>Square  <span class=\"katex--inline\">ABCD</span>  has side length  <span class=\"katex--inline\">1</span> . Points  <span class=\"katex--inline\">P</span> ,  <span class=\"katex--inline\">Q</span> ,  <span class=\"katex--inline\">R</span> , and  <span class=\"katex--inline\">S</span>  each lie on a side of  <span class=\"katex--inline\">ABCD</span>  such that  <span class=\"katex--inline\">APQCRS</span>  is an equilateral convex hexagon with side length  <span class=\"katex--inline\">s</span> . What is  <span class=\"katex--inline\">s</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{\\sqrt{2}}{3} \\qquad \\textbf{(B) } \\frac{1}{2} \\qquad \\textbf{(C) } 2 - \\sqrt{2} \\qquad \\textbf{(D) } 1 - \\frac{\\sqrt{2}}{4} \\qquad \\textbf{(E) } \\frac{2}{3}</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": 1, "problem_name": "2022 AMC 10A Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10A_p06", "prev": "/problem/22_amc10A_p04"}}