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TOT 538 1997 Spring S O3 difference of areas of circle parts

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September 11, 2024
geometryanalytic geometry

Problem Statement

A circle centred at (a,b)(a, b) contains the origin (0,0)(0,0). Denote by S+S^+ the total area of the parts of the circle in the first and third quadrants, and by S−S^- the total area of the parts of the circle in the second and the fourth quadrants. Compute S+−S−S^+ -S^-.
(G Galperin)
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