The tangent line method (TLM) was originally proposed for loudspeaker arrays to generate curvilinear acoustic beams. In this study, the TLM was applied to a microphone array. Based on reciprocity, the TLM-based microphone array can be used to form curvilinear beams. A curvilinear beam is produced as an envelope for the tangent lines. Tangent lines, which are straight beams with different angles, are generated by applying a delay-and-sum (DAS) beamformer. Because the envelope length is specified, the distance discrimination in the sensitivity is better using the TLM than the DAS beamformer. Case studies have indicated that directivity is better in the former TLM than in the latter. The TLM is realizable with fixed delay times for each microphone unless the formation of curvilinear trajectory is altered according to reproduction frequencies. Hence, the same simplicity of implementing the DAS beamformer can be achieved by optimizing the curvilinear trajectory based average frequency. Optimization is conducted such that the acoustic contrast between the focal point and elsewhere is maximized. In summary, the frequency-averaged optimal TLM can be a fixed beamformer with better performance than and the same simplicity as the DAS beamformer.