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We explored exceptional points (EPs) in one dimensional non-Hermitian photonic crystals incorporated with a defect. The defect was asymmetric with respect to the center. Two EPs could be derived by modulating the normalized frequency and the gain-loss coefficient of defect. The reflection coefficient complex phase changed dramatically around EPs, and the change in complex phase was π at EPs. The electric field of EPs was mainly restricted to the defect, which can induce a giant Goos−Hänchen (GH) shift. Moreover, we found a coherent perfect absorption-laser point (CPA-LP) in the structure. A giant GH shift also existed around the CPA-LP. The study may have found applications in highly sensitive sensors.