A circular n-gon is a polygon in the 2-sphere with circular arcs as edges, such that adjacent arcs are tangent at the vertices. I will define a moduli space parameterizing circular n-gons, and for n=2k I will relate this moduli space to a space of k-tuples of pairwise transverse flags. Using this relation we describe a special connected component homeomorphic to a ball, corresponding to the positive component of Fock and Goncharov. This is joint work with Ryan Kirk.