ABCD is a quadrilateral in a circle whose diagonals intersect at right angles. Through O, the centre of the circle,$$GOG'$$ and $$HOH'$$  lines are drawn parallel to AC and BD respectively, meeting AB, CD at G, H and DC, AB produced at $$G'$$, $$H'$$. Prove GH, $$G'H'$$ are parallel to BC and AD respectively.