Compared to existing cone beam computerized tomography (CT) techniques, the reverse geometry based cone beam CT (RGCBCT) can provide projection data with considerably higher SNR, and is convenient in the implementation of exact reconstruction. A novel orthogonal circle and arc orbit for cone beam CT is proposed. Its completeness condition and the application of the Grangeat method are discussed. A flexible orthogonal circle and arcs orbit for RGCBCT together with its completeness condition is proposed. Based on the equivalence between the reverse and traditional imaging geometries, a reconstruction algorithm for RGCBCT and computer simulation results are presented.