Take a look at this picture:

Proposed Geometry Problem 310: Circle Inscribed in a Semicircle, 45 Degrees Angle. College Geometry, SAT Prep. Elearning

I'm not trying to solve the problem in the link, but the picture is relevant to what I'm trying to figure out. If I have a circle inscribed in a semicircle like that, is it true that the points O, C, and E are collinear? If so, how can I prove it?