Problem #PRU-58300

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

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 \(XA\), \(XB\) and \(XC\) is irrational?