Exercise

In figure line $\mathrm{PR}$ touches the circle at point $\mathrm{Q}$. Answer the question with the help of the figure. 

$\angle TAS=65°$, find the measure of $\angle TQS$ and an arc $TS$?

In the figure in a circle with centre $\mathrm{O}$ length of chord $\mathrm{AB}$ is equal to the radius of the circle. If the measure of the $arc\left(ACB\right)$ is $k°$, then find the value of $k$. 

In the figure in a circle with centre $\mathrm{O}$ length of chord $\mathrm{AB}$ is equal to the radius of the circle. If the measure of the $arc\mathrm{AB}$ is $k°$, then find the value of $k$.

If two circles with radii $8 \mathrm{cm}$ and $3 \mathrm{cm}$ respectively touch externally, then find the distance (in $\mathrm{cm}$) between their centres.

Two circles of radii $5.5 \mathrm{cm}$ and $3.3 \mathrm{cm}$ respectively touch each other externally. The distance between their centres is

In the given figure$, \mathrm{m}(arc\mathrm{NS})=125°$,  $\mathrm{m}(arcEF)=37°$, the measure $\angle \mathrm{NMS}$ is $k°$. Find the value of $k$.

In the figure, quadrilateral $\mathrm{PQRS}$ is cyclic. Side $\mathrm{PQ}\cong$Side $\mathrm{RQ}.\angle \mathrm{PSR}=110°$ if the measure of $\angle \mathrm{PQR}$ is $\mathrm{k}°$, then find the value of $\mathrm{k}$.

In the given figure, chords $\mathrm{AC}$ and $\mathrm{DE}$  intersects at $\mathrm{B}$. If $\angle \mathrm{ABE}=108°$ $\mathrm{m}(arc\mathrm{AE})=95°$, $\mathrm{m}(arcDC)$ is $k°$. Find the value of $k$.