We analyze the electromagnetic field of a small bunch that uniformly moves in a circular waveguide and transverses a boundary between an area filled up with a strongly magnetized cold plasma and a vacuum area. Such plasma is described with a diagonal dielectric permittivity tensor. The investigation of the waveguide mode components is performed analytically and numerically. The Cherenkov radiation in the filled area of the waveguide and the Cherenkov-transition radiation (CTR) in the vacuum area are under investigation. The conditions of excitation of CR and the CTR peculiarities are obtained. Typical graphics for the field of the excited waveguide mode are presented.