Smoothing the Interfaces of Overlapping 2D Shapes

[orchidacaea]

Hi,
I was wondering how you would smooth out the intersection of two 2D shapes' overlap. For example, if I had intersecting shapes like those in the image above would it be possible to smooth the interface circled in red so that it wouldn't have a corner i.e. a non-differentiable intersection point?

Thanks

[Dave R]

Draw an arc?

I don't know if you want them but you can get smoother curves all the way around if you increase the number of sides on the circle and the circle you used to create the half-ellipse.