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The paper describes an extended algorithm for solving the point-in-polygon problem. The polygon in this case consists of straight edges and also from circular arcs. The algorithm uses the classical ray intersection method. The difference is that we now have two types of geometric objects to test for intersections. Processing is done with simple and efficient tests, which quickly answer our question. By the use of appropriate data structure, this task can be done safely and easily. Despite the extension of the classical ray intersection method, the algorithm still runs in linear time complexity.