On the plane is give a broken line ABCD in which AB=BC=CD=1, and AD is not equal to 1. The positions of B and C are fixed but A and D change their positions in turn according to the following rule (preserving the distance rules given): the point A is reflected with respect to the line BD, then D is reflected with respect to the line AC (in which A occupies its new position), then A is reflected with respect to the line BD (D occupying its new position), D is reflected with respect to the line AC, and so on. Prove that after several steps A and D coincide with their initial positions.(M Kontzewich) geometrygeometric transformationreflectionbroken linecombinatoricscombinatorial geometry