MathDB

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.

Problem Statement