ILL 1976 Problem 7

Let $P$ be a fixed point and $T$ a given triangle that contains the point $P$ . Translate the triangle $T$ by a given vector $\bold{v}$ and denote by $T'$ this new triangle. Let $r, R$ , respectively, be the radii of the smallest disks centered at $P$ that contain the triangles $T , T'$ , respectively. Prove that $r + |\bold{v}| \leq 3R$ and find an example to show that equality can occur.