(a)[5]
On a circle with centre $O$, A, B, C and D are points on the circumference. AOD and OCE are straight lines. DE is tangent to the circle at D. Given that $\angle ABC = 126^\circ$ and $DE = 10.5\,\text{cm}$, Calculate the radius of the circle.
(b)[5]
On another circle with centre $O$, P and Q are points on the circumference. The minor sector $POQ$ has angle $82^\circ$. The minor arc $PQ$ measures $7.3\,\text{cm}$. Calculate the area of the major sector.