MathNet 2017-part-03 — 176 problems (EN–VI) Question 130

Let $a$ and $b$ be two positive real numbers. Consider a regular hexagon with side $a$, and construct on its sides six rectangles with sides $a$ and $b$, placed externally to the hexagon. The twelve new vertices lie on a circle. We repeat the previous operation, but swapping the values of $a$ and $b$: that is, we start from a regular hexagon with side $b$ and construct on it, again externally to the hexagon, six rectangles with sides $a$ and $b$. We obtain that the twelve new vertices lie on a second circle.
Prove that the two circles have the same radius.