On two sides of right angle with vertex in point O we choose points A and B, |OA|=|OB|. On arc AB with center in O we choose point P. Through that point we draw line parallel with AB which intersects OA in point C, and OB in point D. Prove that |PC|^{2}+|PD|^{2}=|AB|^{2.}

I hope you understand my question. I find a lot of similar and right triangles but always get stuck.