Angle in the alternate segment

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.

To download this Geogebra file click here.