Ok so I have this made from half a cylinder and I have cut out the faces were I want a door to be:

I want to create something like this:

You see how the doorway is part of the cylindrical shape and has its own arch? I would then extrude the edges when I have created the arch. I first tried manually adding edge loops but it just did not look right. How can I create a nice curved arch from the square doorway in the first image?