(a) In Fig. $1, AB$ is diameter of a circle centered at $O \cdot BC$ is tangent to the circle at $B$. If $OP$ bisects the chord $AD$ and $\angle AOP = 60^{\circ}$, then find $m\angle C$.(b) In Fig. 2, XAY is a tangent to the circle centered at $O$. If $\angle ABO = 40^{\circ}$, then find $m\angle BAY$ and $m\angle AOB$.