Two circles touch each other externally at $\mathrm{P}$. Prove that the common tangent bisects the other two common tangents. 

In the fig., $PQ$ and $PR$ are tangents to the circle with centre $O$. If $\angle \mathrm{QOR}=120°$, then find $\angle \mathrm{OPR}$. (Write the answer without degree symbol)

In the figure $\mathrm{PQ}$ and $\mathrm{PR}$ are tangents to the circle with centre $\mathrm{O}$. If $\angle \mathrm{QOR} =120°$, then find $\angle \mathrm{QPR}$.

In the fig., $\mathrm{ABC}$ is a right triangle right-angled at $\mathrm{B}$ such that $\mathrm{BC}=6 \mathrm{cm}$ and $\mathrm{AB}=8 \mathrm{cm}$. If the radius of its incircle is $k \mathrm{cm}$, then find the value of $k$.