There is a numerical solution, and there may not be a closed solution for all n-gons. The generalization for n-gons which are not convex is not about "the centre of the circle being inside the n-gon" ... a) the n-gon may circle the centre 'k' times (including k = 0) b) the n-gon may have edges that 'double back', e.g: ABC is a triangle, A' is 'very near' A, B' very near B ABA'B'C is a pentagon with an area very near ABC's. [ Does the concept of area need more careful definition? ] It would appear that one needs a diagram of the n-gon as 'evidence' of the clockwise/counterclockwise 'direction' of the edges ... or can that be deduced too? Guy