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The Isoperimetric Theorem states that for a planar region of given perimeter, the circle encloses the maximum area. In this paper, we determine the shape that maximizes area when the boundary is constrained to have length L and to contain two points x units apart. For L ≥ xπ maximum area is clearly attained by a circle of diameter L π containing the points. When 2x <L<xπ, we prove that the maximum area is attained when the boundary is two congruent circular arcs. We also consider the case of three equidistant points x units from each other. For some constant M, when3x<L<M, the maximum area is attained when the boundary is three congruent circular arcs. When L ≥ M, themaximumareais attained when the boundary consists of two congruent circular arcs of length a and a third complementary circular arc of length b, whereb ≥ a and a + b forms a circle.