A billiard ball in a rectangular pool table
Source: IMO LongList 1982 - P11
March 16, 2011
geometrygeometric transformationreflectionrectangleanalytic geometrygraphing linesslope
Problem Statement
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 and . 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 and be for this to happen?