{"status": "success", "data": {"description_md": "Let $S$ be the set of all points $(x,y)$ in the coordinate plane such that $0\\leq x\\leq \\frac\\pi 2$ and $0\\leq y\\leq \\frac\\pi 2$. What is the area of the subset of $S$ for which $\\sin^2 x - \\sin x\\sin y + \\sin^2 y\\le \\frac 34$?\n\n$\\mathrm{(A)}\\ \\frac {\\pi^2}9
\\qquad
\\mathrm{(B)}\\ \\frac {\\pi^2}8
\\qquad
\\mathrm{(C)}\\ \\frac {\\pi^2}6
\\qquad
\\mathrm{(D)}\\ \\frac {3\\pi^2}{16}
\\qquad
\\mathrm{(E)}\\ \\frac {2\\pi^2}9$\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 S be the set of all points (x,y) in the coordinate plane such that 0\\leq x\\leq \\frac\\pi 2 and 0\\leq y\\leq \\frac\\pi 2 . What is the area of the subset of S for which \\sin^2 x - \\sin x\\sin y + \\sin^2 y\\le \\frac 34 ?

\\mathrm{(A)}\\ \\frac {\\pi^2}9\\qquad\\mathrm{(B)}\\ \\frac {\\pi^2}8\\qquad\\mathrm{(C)}\\ \\frac {\\pi^2}6\\qquad\\mathrm{(D)}\\ \\frac {3\\pi^2}{16} \\qquad\\mathrm{(E)}\\ \\frac {2\\pi^2}9

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": "2006 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc12B_p25", "prev": "/problem/06_amc12B_p23"}}