Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

In the figure, $\mathrm{PQ}$ is tangent at a point $\mathrm{R}$ of the circle with centre $\mathrm{O}$. If $\mathrm{\angle }\mathrm{T}\mathrm{R}\mathrm{Q}=30°,$ find $\mathrm{m}\mathrm{\angle }\mathrm{P}\mathrm{R}\mathrm{S}.$

In the given figure, $\mathrm{ABC}$ is a right triangle right-angled at $\mathrm{B}$ such that $\mathrm{BC}=6 \mathrm{cm}$ and $\mathrm{AB}=8 \mathrm{cm}.$ Find the radius of its incircle.