{"status": "success", "data": {"description_md": "Let $ABCD$ be a unit square. Let $Q_1$ be the midpoint of $\\overline{CD}$. For $i=1,2,\\ldots,$ let $P_i$ be the intersection of $\\overline{AQ_i}$ and $\\overline{BD}$, and let $Q_{i+1}$ be the foot of the perpendicular from $P_i$ to $\\overline{CD}$. What is \n\n$$\\sum_{i=1}^{\\infty} \\text{Area of } \\triangle DQ_i P_i \\, ?$$\n\n$\\textbf{(A)}\\ \\frac{1}{6} \\qquad
\\textbf{(B)}\\ \\frac{1}{4} \\qquad
\\textbf{(C)}\\ \\frac{1}{3} \\qquad
\\textbf{(D)}\\ \\frac{1}{2} \\qquad
\\textbf{(E)}\\ 1$\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": "

Let ABCD be a unit square. Let Q_1 be the midpoint of \\overline{CD} . For i=1,2,\\ldots, let P_i be the intersection of \\overline{AQ_i} and \\overline{BD} , and let Q_{i+1} be the foot of the perpendicular from P_i to \\overline{CD} . What is

\\sum_{i=1}^{\\infty} \\text{Area of } \\triangle DQ_i P_i \\, ?

\\textbf{(A)}\\ \\frac{1}{6} \\qquad\\textbf{(B)}\\ \\frac{1}{4} \\qquad\\textbf{(C)}\\ \\frac{1}{3} \\qquad\\textbf{(D)}\\ \\frac{1}{2} \\qquad\\textbf{(E)}\\ 1

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": 5, "problem_name": "2016 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12B_p22", "prev": "/problem/16_amc12B_p20"}}