Points A, B, and C are placed on a circle centered at O as in the following diagram.

If AC = BC and angle OAC = 38 degrees, then how many degrees are in angle AOB?

OAC is an isocles triangle with base angles 38. Therefore, anle AOC is 104 degrees. Since triangle OAC is congruent to triangle OCB by SSS congruence, angle COB is also 104 degrees.

The measure of angle AOB is 208 degrees.