IMO 1982 LL BRA11

A rectangular pool table has a hole at each of three of its

IMO 1982 LL BRA11

Origin: BRA

Problem

A rectangular pool table has a hole at each of three of its corners. The lengths of sides of the table are the real numbers a and b. A billiard ball is shot from the fourth corner along its angle bisector. The ball falls in one of the holes. What should the relation between a and b be for this to happen?