Bicentric heptagons

A bicentric heptagon is one for which all vertices lie on a circle, and for which all edges are tangential to another circle. If \(R\) and \(r\) are the radii of the outer and inner circles respectively, and \(d\) is the distance between their centres, there is an expression which relates the three values when a bicentric heptagon can be formed. To start, define \[ a = \frac{1}{R+d},\quad b =…