AC is a chord, and their is a tangent drawn at C. The angle between AC and the tangent is the same as that at the point B. B is a point in the *alternate segment* (ie the one on the other side of AC to the angle being considered).

Obviously this also applies to the chord BC and the angle at A in its alternate segment.

Have a look at the *Hint*; it is a case of radius meeting tangent, isosceles triangle and finally angle at the centre is double angle at circumference.