A circle is divided up by the points \(A, B, C, D\) so that \({\smile}{AB}:{\smile}{BC}:{\smile}{CD}:{\smile}{DA} = 2: 3: 5: 6\). The chords \(AC\) and \(BD\) intersect at point \(M\). Find the angle \(AMB\).
A circle is divided up by the points \(A\), \(B\), \(C\), \(D\) so that \({\smile}{AB}:{\smile}{BC}:{\smile}{CD}:{\smile}{DA} = 3: 2: 13: 7\). The chords \(AD\) and \(BC\) are continued until their intersection at point \(M\). Find the angle \(AMB\).
The bisector of the outer corner at the vertex \(C\) of the triangle \(ABC\) intersects the circumscribed circle at the point \(D\). Prove that \(AD = BD\).
On the circle, the points \(A, B, C\) and \(D\) are given. The lines \(AB\) and \(CD\) intersect at the point \(M\). Prove that \(AC \times AD / AM = BC \times BD / BM\).
In the triangle \(ABC\), the height \(AH\) is drawn; \(O\) is the center of the circumscribed circle. Prove that \(\angle OAH = | \angle B - \angle C\)|.