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covering a disk with other disks

Source: France 1993 P4

May 12, 2021
geometry

Problem Statement

We are given a disk D\mathcal D of radius 11 in the plane.
(a) Prove that D\mathcal D cannot be covered with two disks of radii r<1r<1. (b) Prove that, for some r<1r<1, D\mathcal D can be covered with three disks of radius rr. What is the smallest such rr?
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