Quadrilateral with Orthogonal Diagonals Induces a Circle

This is a quadrilateral with orthogonal (i.e. at right angle) diagonals. The point of intersection of the diagonals is reflected through each edge of the quadrilateral. It turns out that the four reflected points all lie on a circle! You can play with moving the vertices of the quadrilateral along the diagonals. I am getting this from Tristan Needham's book, Visual Complex Analysis, pages 137-138. The proof uses inversion in a circle.