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