Let centre of square (point of intersection of diagonals) be origin.
Vertices of square are A(1, 1), B(–1, 1), C(–1, –1) and D(1, –1). Radius of circumscribed or inscribed circles are 2 and 1, respectively.
Let any point P and Q on circumscribed and inscribed circles, respectively, be (√2 cosα,√2 sin α) and (cosβ, sinβ). Therefore,