IT-CESENATICO 2017 Problem 1

Let $a$ and $b$ be positive real numbers. Consider a regular hexagon of side $a$ , and build externally on its sides six rectangles of sides $a$ and $b$ . The new twelve vertices lie on a circle. Now repeat the same construction, but this time exchanging the roles of $a$ and $b$ ; namely; we start with a regular hexagon of side $b$ and we build externally on its sides six rectangles of sides $a$ and $b$ . The new twelve vertices lie on another circle. Show that the two circles have the same radius.