{"status": "success", "data": {"description_md": "A square piece of paper has side length $1$ and vertices $A,B,C,$ and $D$ in that order. As shown in the figure, the paper is folded so that vertex $C$ meets edge $\\overline{AD}$ at point $C'$, and edge $\\overline{AB}$ at point $E$. Suppose that $C'D = \\frac{1}{3}$. What is the perimeter of triangle $\\bigtriangleup AEC' ?$\n\n
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\n\n$\\textbf{(A)} ~2 \\qquad\\textbf{(B)} ~1+\\frac{2}{3}\\sqrt{3} \\qquad\\textbf{(C)} ~\\frac{13}{6} \\qquad\\textbf{(D)} ~1 + \\frac{3}{4}\\sqrt{3} \\qquad\\textbf{(E)} ~\\frac{7}{3}$", "description_html": "

A square piece of paper has side length 1 and vertices A,B,C, and D in that order. As shown in the figure, the paper is folded so that vertex C meets edge \\overline{AD} at point C' , and edge \\overline{AB} at point E . Suppose that C'D = \\frac{1}{3} . What is the perimeter of triangle \\bigtriangleup AEC' ?

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\\textbf{(A)} ~2 \\qquad\\textbf{(B)} ~1+\\frac{2}{3}\\sqrt{3} \\qquad\\textbf{(C)} ~\\frac{13}{6} \\qquad\\textbf{(D)} ~1 + \\frac{3}{4}\\sqrt{3} \\qquad\\textbf{(E)} ~\\frac{7}{3}

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Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2021 AMC 10B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc10B_p22", "prev": "/problem/21_amc10B_p20"}}