Consider a convex quadrilateral with vertices at p, q, r and s and on each side draw a square lying outside the given quadrilateral, as in the picture below. Let p,q,r and s be the centers of those squares:
a) Find expressions for p,q,r and s in terms of a,b,c and d.
b) Prove that the line segment between p and r is perpendicular and equal in length to the line segment between q and s.
