The bisector of the outer corner at the vertex \(C\) of the triangle \(ABC\) intersects the circumscribed circle at the point \(D\). Prove that \(AD = BD\).
In the triangle \(ABC\), the height \(AH\) is drawn; \(O\) is the center of the circumscribed circle. Prove that \(\angle OAH = | \angle B - \angle C\)|.