Question 33
Let $ABCD$ be a square with side length $1$.
a) Prove that there is no point $M$ in the plane of the square such that the lengths of the segments $MA$, $MB$, $MC$, and $MD$ are natural numbers.
b) Find the points $M$ in space such that the lengths of the segments $MA$, $MB$, $MC$, and $MD$ are natural numbers.
a) Prove that there is no point $M$ in the plane of the square such that the lengths of the segments $MA$, $MB$, $MC$, and $MD$ are natural numbers.
b) Find the points $M$ in space such that the lengths of the segments $MA$, $MB$, $MC$, and $MD$ are natural numbers.