In the adjoining figure, $\mathrm{O}$ is the centre of the circle. From point $\mathrm{R}$ segment $\mathrm{RM}$ and segment $\mathrm{RN}$ are tangent segments touching the circle at $\mathrm{M}$ and $\mathrm{N}$. If $\left(\mathrm{OR}\right)=10 \mathrm{cm}$ and radius of the circle $=5 \mathrm{cm}$. If is the measure of $\angle \mathrm{MRO}$ is $k°$, then find the value of $k$.

 

In the adjoining figure, $\mathrm{O}$ is the centre of the circle. From point $\mathrm{R}$ segment $\mathrm{RM}$ and segment $\mathrm{RN}$ are tangent segments touching the circle at $\mathrm{M}$ and $\mathrm{N}$. If $\left(\mathrm{OR}\right)=10 \mathrm{cm}$ and radius of the circle $=5 \mathrm{cm}$, if the measure of $\angle \mathrm{MRN}$ is $k$ degree, then find the value of $k$.

Segment $\mathrm{RM}$ and segment $\mathrm{RN}$ are tangent segments of a circle with centre $\mathrm{O}$ Prove that segment $\mathrm{OR}$ bisects $\angle \mathrm{MRN}$ as well as $\angle \mathrm{MON}$

In the figure the circles with centres $\mathrm{P}$ and $\mathrm{Q}$ touch each other at $\mathrm{R}$. A line passing through $\mathrm{R}$ meets the circles at $\mathrm{A}$ and $\mathrm{B}$ respectively. Prove that segment $\mathrm{AP}\Vert$ segment $\mathrm{BQ}$.