A straight line AB touches the ellipse x2/a2 + y2/b2 = 1 & the circle x2+y2 =r2 where a >r > b. PQ is a focal chord of the ellipse. If PQ be parallel to AB and cuts the circle in P & Q, find the length of the perpendicular drawn from the centre of the ellipse to PQ. Hence show that PQ = 2b.
