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Circle containing a path of length 1

Source: 2022 Grosman Mathematical Olympiad P3

September 22, 2022
combinatoricscombinatorial geometry

Problem Statement

An ant crawled a total distance of 11 in the plane and returned to its original position (so that its path is a closed loop of length 11; the width is considered to be 00). Prove that there is a circle of radius 14\frac{1}{4} containing the path.
Illustration of an example path:
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