Problem #PRU-58300

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

13–15 3.0

Problem

Do there exist three points $A$ , $B$ and $C$ on the plane such that for any point $X$ the length of at least one of the segments $X A$ , $X B$ and $X C$ is irrational?

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