Using TikZ, how can I fill in an angle of a given polygon with a colored arc? For example, given the triangle
\filldraw[fill=yellow, draw=black] (10,0) -- (-2,9) -- (4,-3) -- (10,0);
I'd like a blue arc of radius 1 centered on (10,0) sweeping out the angle bounded by the sides of the triangle.
Edit: I forgot an important part of my question, which (I think) makes the links provided in the comments insufficient.
How can I fill only half the angle with a shaded arc?