Question 102
A number $r_X \gt 0$ is assigned to any point $X$ in the plane such that $2|r_X - r_Y| \le |XY|$ for any two points $X$ and $Y$. A cricket can jump from $X$ to $Y$ if $r_X = |XY|$. Prove that for any two points $X$ and $Y$ the cricket can move from $X$ to $Y$ by finite number of jumps.