AMC 10 Step by Step
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2016 AMC 10BProblem 21P21-25~6 minPrint
CirclesAbsolute Value & InequalitiesCoordinate GeometryApply an identity: SFFT, sum of squares, difference of cubes, VietaCut the figure into known shapes (triangles, rectangles, sectors)Exploit symmetry to reduce work or pair up objects

What is the area of the region enclosed by the graph of the equation x2+y2=∣x∣+∣y∣?x^2+y^2=|x|+|y|?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.