{"status": "success", "data": {"description_md": "In the diagram, line segment $PS$ has length 4. Points $Q$ and $R$ are on line segment $PS$. Four semi-circles are drawn on the same side of $PS$. The diameters of these semi-circles are $PS$, $PQ$, $QR$, and $RS$. The region inside the largest semi-circle and outside the three smaller semi-circles is shaded. What is the area of a square whose perimeter equals the perimeter of the shaded region?\n\n
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\n\n$\\text{(A)}\\ 4\\qquad\\text{(B)}\\ \\pi\\qquad\\text{(C)}\\ \\pi^2\\qquad\\text{(D)}\\ 2\\pi^2\\qquad\\text{(E)}\\ \\dfrac{\\pi^2}{4}$\n\n___\n\n**[Pascal](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "

In the diagram, line segment PS has length 4. Points Q and R are on line segment PS. Four semi-circles are drawn on the same side of PS. The diameters of these semi-circles are PS, PQ, QR, and RS. The region inside the largest semi-circle and outside the three smaller semi-circles is shaded. What is the area of a square whose perimeter equals the perimeter of the shaded region?

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\"figure\"
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\\text{(A)}\\ 4\\qquad\\text{(B)}\\ \\pi\\qquad\\text{(C)}\\ \\pi^2\\qquad\\text{(D)}\\ 2\\pi^2\\qquad\\text{(E)}\\ \\dfrac{\\pi^2}{4}

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Pascal, by CEMC, is licensed under the CC BY-NC 3.0 DEED. They are not affiliated with or endorse TopsOJ in any way.

\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2014 Pascal Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/14_pascal_p21", "prev": "/problem/14_pascal_p19"}}