Question 55098
I think you're on the right track. I'm going to get away from the trig part, though.

Here's the tack I think you should take.

1) Find the midpoint of chord AB. I'll call that point M.
2) Prove that the line from C through M must also go through the midpoint of your arc(if its a geometry class. It may be acceptable to just throw that statement on the table in an Algebra class).
3) Find the equation of the line that passes through M and C
4) figure out where the line intersects your arc. 

Let me know if that's enough direction for ya...