(a) In Fig. 1, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠ AOP =60^°, then find m ∠…

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

Fig. $\displaystyle 1$

In Fig. $\displaystyle 2$, XAY is a tangent to the circle centered at O. If $\displaystyle \angle \mathrm{ABO}=40^{\circ}$, then find $\displaystyle \mathrm{m} \angle \mathrm{BAY}$ and $\displaystyle \mathrm{m} \angle \mathrm{AOB}$.