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area set of points in the plane belonging to at least two of the disks >R^2/8

Source: Romania IMO TST 1990 p5

February 19, 2020
geometrycircumcirclecirclesareaGeometric Inequalitiesinequalities

Problem Statement

Let OO be the circumcenter of an acute triangle ABCABC and RR be its circumcenter. Consider the disks having OA,OB,OCOA,OB,OC as diameters, and let Δ\Delta be the set of points in the plane belonging to at least two of the disks. Prove that the area of Δ\Delta is greater than R2/8R^2/8.
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