triangle pool table
Source: Polish MO Finals 1971 p2
August 22, 2024
geometrygeometric transformationreflection
Problem Statement
A pool table has the shape of a triangle whose angles are in a rational ratio. A ball positioned at an interior point of the table is hit by a stick. The ball reflects from the sides of the triangle according to the law of reflection. Prove that the ball will move only along a finite number of segments. (It is assumed that the ball does not reach the vertices of the triangle.)