Angle Properties of Circles: Thales' Theorem and Subtended Arcs

In the figure below, points \(A\), \(B\), \(C\) and \(D\) all lie on the circumference of the circle with centre \(O\).
\(AD\) is the diameter of the circle.
Find the value of

1. \(x\),
2. \(y\),
3. \(z\).

Diagram correction: the interior centre label should be \(O\), not \(B\). The point \(B\) on the circumference retains its label.