Regional problem · Geometry

Two circles touch each other internally at a point \(A\). Let \(AB\) be a diameter of the larger circle. Through the other endpoint \(B\) of this diameter a line is drawn which touches the smaller circle at a point \(C\) and meets the larger circle again at a point \(D\).

Prove that the line \(AC\) bisects the angle \(BAD\).

The two circles touch internally at \(A\), the segment \(AB\) is a diameter of the larger one, the line through \(B\) touches the smaller circle at \(C\), and \(D\) is where it meets the larger circle a second time.