Is it possible in a plane mark $10$ red, $10$ blue and $10$ green points (all distinct) such that three conditions hold: $i)$ For every red point $A$ there exists a blue point closer to point $A$ than any other green point $ii)$ For every blue point $B$ there exists a green point closer to point $B$ than any other red point $iii)$ For every green point $C$ there exists a red point closer to point $C$ than any other blue point