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Problem 4

Part of 1993 French Mathematical Olympiad

Problems(1)

covering a disk with other disks

Source: France 1993 P4

5/12/2021
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?
geometry