We present accurate analytical solutions of the lineshapes of birefringence (rotation) and dichroism (absorption) spectroscopy for a circular anisotropic medium composed of atoms of the transition $J_g=0{ ightarrow}J_e=1$. The susceptibility of a weak probe beam was analytically calculated and was averaged over a Maxwell-Boltzmann velocity distribution. The lineshapes of the two spectroscopies were then presented in analytical forms at arbitrary values of the linewidths of the inhomogeneous (Doppler) broadening and the homogeneous (natural) broadening of the atoms.