MathDB

9.7

Part of 1998 All-Russian Olympiad Regional Round

Problems(1)

regular 1998-gon billiard - All-Russian MO 1998 Regional (R4) 9.7

Source:

9/17/2024
Given a billiard in the form of a regular 19981998-gon A1A2...A1998A_1A_2...A_{1998}. A ball was released from the midpoint of side A1A2A_1A_2, which, reflected therefore from sides A2A3A_2A_3, A3A4A_3A_4, . . . , A1998A1A_{1998}A_1 (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 19981998-gon.
combinatoricscombinatorial geometrygeometryregular polygon