{"status": "success", "data": {"description_md": "Let $ABCDE$ be an equiangular convex pentagon of perimeter $1$. The pairwise intersections of the lines that extend the sides of the pentagon determine a five-pointed star polygon. Let $s$ be the perimeter of this star. What is the difference between the maximum and the minimum possible values of $s$?\n\n$\\textbf{(A)}\\ 0 \\qquad \\textbf{(B)}\\ \\frac{1}{2} \\qquad \\textbf{(C)}\\ \\frac{\\sqrt{5}-1}{2} \\qquad \\textbf{(D)}\\  \\frac{\\sqrt{5}+1}{2} \\qquad \\textbf{(E)}\\ \\sqrt{5}$\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>Let  <span class=\"katex--inline\">ABCDE</span>  be an equiangular convex pentagon of perimeter  <span class=\"katex--inline\">1</span> . The pairwise intersections of the lines that extend the sides of the pentagon determine a five-pointed star polygon. Let  <span class=\"katex--inline\">s</span>  be the perimeter of this star. What is the difference between the maximum and the minimum possible values of  <span class=\"katex--inline\">s</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 0 \\qquad \\textbf{(B)}\\ \\frac{1}{2} \\qquad \\textbf{(C)}\\ \\frac{\\sqrt{5}-1}{2} \\qquad \\textbf{(D)}\\  \\frac{\\sqrt{5}+1}{2} \\qquad \\textbf{(E)}\\ \\sqrt{5}</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": "2013 AMC 12B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12B_p17", "prev": "/problem/13_amc12B_p15"}}