In the figure, $AB$ and $CD$ are common tangents to two circles of unequal radii. Prove that $AB=CD$.

 

In the figure, $CP$ and $CQ$ are tangents to a circle with centre $O$. $ARB$ is another tangent touching the circle at $R$. If $CP=11 \mathrm{cm}$ and $BC=7 \mathrm{cm}$, then find the length of $BR$.
    

In the figure, $CP$ and $CQ$ are tangents from an external point $C$ to a circle with centre $O$. $AB$ is another tangent which touches the circle at $R$. If $CP=11 \mathrm{cm}$ and $BR=4 \mathrm{cm}$, find the length of $BC$.

In the figure, $△ABC$ is circumscribing a circle. Find the length of $BC$ in $\mathrm{cm}$.

In the figure, $PA$ and $PB$ are tangents to the circle with centre $O$ such that $\angle APB=50°$. Write the measure of $\angle OAB$.

In the figure, $BOA$ is a diameter of a centre and the tangent at a point $P$ meets $BA$ (produced) at $T$. If $\angle PBO=30°,$ then $\angle PTA$ is equal to $30°$. Prove it.
  

It is possible to draw a maximum of one tangent to a circle from a point, which lies in the exterior of the circle. 

One and only one tangent can be drawn from a point on the circle.