Proving a Convex Quadrilateral is a Square with Internal Point O as its Center

[lolerlol]

Homework Statement

Let O be an internal point of a convex quaddrilateral PQRS whose area is A.

Prove that, if 2A = OP^2 + OQ^2 + OR^2 + OS^2, then PQRS is a square with O as its centre

Homework Equations

The Attempt at a Solution

I have no idea where to start, except that I know that I need to use 1/2 ab sin C

 

[wildman]

Forget the 1/2 ab sin C for now. Draw a picture and think Pythagorean Theorum.

 

[wildman]

how does PQ, QR, RS and SP relate? Are they the same or different? If you bisect the segment PQ and square the result, how does that relate to the square of the segment OP? How about to the area of the square?