This expository paper consists of two parts. In the first half we study circles in a complex projective space and give a characterization of homogeneous real hypersurfaces in a complex projective space by using geometric properties of circles. In the latter half we study geodesics of geodesic spheres, which are the simplest real hypersurfaces in a complex projective space, and investigate their length spectrum in detail. Finally we characterize real and complex space forms from this point of view.