Brass asked the following question in 2005: For n ? 5 odd, what is the maximum perimeter of a simple n-gon contained in a Euclidean unit disk? In 2009, Audet, Hansen and Messine answered this question, and showed that the optimal configuration is an isosceles triangle with a multiple edge, inscribed in the disk. In this note we give a shorter and simpler proof of their result, which we generalize also for hyperbolic disks, and for spherical disks of sufficiently small radii. Furthermore, we present results about other variants of the original question, and introduce some open problems.