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This paper considers the scattering of time-harmonic acoustic plane waves by a mixed scatterer. Such a scatterer is given as the union of a penetrable homogeneous medium with compact support and an open arc. Firstly, the well-posedness of the direct problem is established by the boundary integral method. Then, we study the factorization method for recovering the shape of the mixed scatterer. Furthermore, some numerical experiments are presented to demonstrate the feasibility and effectiveness of our approach.

The factorization method to reconstruct a combination of penetrable obstacle and arc