5

Part of 2008 German National Olympiad

Problems(1)

Sum of circumferences is 10 => Line intersects 4 disks

Source: German DEMO 2008, grade 11-13, round 4, problem 5

Inside a square of sidelength

1

there are finitely many disks that are allowed to overlap. The sum of all circumferences is

10

. Show that there is a line intersecting or touching at least

4

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