regular 1998-gon billiard - All-Russian MO 1998 Regional (R4) 9.7
Source:
September 17, 2024
combinatoricscombinatorial geometrygeometryregular polygon
Problem Statement
Given a billiard in the form of a regular -gon . A ball was released from the midpoint of side , which, reflected therefore from sides , , . . . , (according to the law, the angle of incidence is equal to the angle of reflection), returned to the starting point. Prove that the trajectory of the ball is a regular -gon.