Question 46
A set $S$ of four distinct points is given in the plane. It is known that for any point $X \in S$ the remaining points can be denoted by $Y, Z$ and $W$ so that
$$
|X Y| = |X Z| + |X W|.
$$
Prove that all the four points lie on a line.
$$
|X Y| = |X Z| + |X W|.
$$
Prove that all the four points lie on a line.