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three circles, minimal set of points

Source: French MO 1995 P3

April 22, 2021
geometry

Problem Statement

Consider three circles in the plane Γ1,Γ2,Γ3\Gamma_1,\Gamma_2,\Gamma_3 of radii RR passing through a point OO, and denote by D\mathfrak D the set of points of the plane which belong to at least two of these circles. Find the position of Γ1,Γ2,Γ3\Gamma_1,\Gamma_2,\Gamma_3 for which the area of D\mathfrak D is the minimum possible. Justify your answer.
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