Constructing Poncelet Quadrilaterals using inversive geometry

In the diagram above, you are given a circle with centre at \(O\) and a point \(R\) on the circle. Inside the circle is a point \(P\). Two perpendicular lines are drawn through the point \(P\), and these intersect the blue circle at points \(A\), \(B\), \(C\) and \(D\). The tangents to the circle at the points \(A\), \(B\), \(C\) and \(D\) will intersect at points \(W\), \(X\), \(Y\) and \(Z\). It is a theorem (which we will prove in Tutorial 10 and Homework 2) that \(WXYZ\) is a cyclic quadrilateral, and therefore we have a Poncelet quadrilateral which is inscribed in the red cirlce and tangent to the blue circle.

Moving the points \(O\), \(P\) and \(R\) will automatically resize the two circles such that they admit this Poncelet quadrilateral. The proof that \(WXYZ\) is a cyclic quadrilateral uses inversive geometry, and is explained in more detail here.