draw a circle.
draw any cyclic quadrilateral in it.
name it A-B-C-D.
join BD and AC (diagonals)


PROVE THAT:
AC x BD= AB x CD + BC x AD

I think the easiest way to tackle this problem is taking the sides AB, BC, CD and DA to be equal. You therefore take a square. The length of the diagonal is always \sqrt2 times the side of the square, from Pythagoras' Theorem. Then, using your drawing, let x be the length of the side of your square the diagonal will be x\sqrt2 and use those to show the proof.