The coherent exciton plays an important role in the photosynthetic primary process, and its functions are deeply dependent on the orientation arrangements of local transition dipole moments (TDMs). We theoretically and systematically study the physical property of the coherent exciton at different orientation arrangements of the local TDMs in circular light-harvesting (LH) complexes. Especially, if the orientation arrangements are different, the delocalized TDMs of the coherent excitons and the energy locations of the optically active coherent excitons (OACEs) can be obviously different, and then there are more manners to capture, store and transfer light energy in and between LH complexes.Similarly, if the orientation arrangements are altered, light absorption and radiative intensities can be converted fully between the OACEs in the upper and lower coherent exciton bands, and then the blue and red shifts of the absorption and radiative bands of the pigment molecules can occur simultaneously at some orientation arrangements. If the systems are in the vicinities of the critical orientation arrangements, the weak static disorder or small thermal excitation can destroy the coherent electronic excitations, and then the coherent exciton cannot exist any more.