Question 85
In the plane there are two triangles $ABC$ and $A'B'C'$. All side lengths of triangle $ABC$ are at least $a$, and all side lengths of triangle $A'B'C'$ are at least $a'$. Prove that one can always choose one vertex from each of the two triangles so that their distance is at least $\sqrt{\frac{a^2+a'^2}{3}}$.