In the figure, P and Q are the points of intersection of two circles with centres O and O′. If straight lines, APB and CQD are parallel to OO′, then what is the ratio of OO′ and AB?
Draw OM⊥AP and O′N⊥PB.
Now, quadrilateral OO′NM is a rectangle, since, all of its angles are 90∘
We know that, perpendicular from the centre of the circle to the chord bisects the chord, therefore