Two circles with centres O and O′ intersect at two points A and B. A line PQ is drawn parallel to OO′ through A or B, intersecting the circles at P and Q. Prove that PQ=2OO′.

Two circles with centres O and O′ intersect at two points A and B. A

1.	Two circles with centres O and O′ intersect at two points A and B. A line PQ is drawn parallel to OO′ through A or B, intersecting the circles at P and Q. Prove that PQ=2OO′.
Answer» Two circles with centres $O$ and $O^{'}$ intersect at two points $A$ and $B$ . $A$ line $P Q$ is drawn parallel to $O O^{'}$ through $A$ or $B$ , intersecting the circles at $P$ and $Q .$ Prove that $P Q = 2 O O^{'} .$