Exercise 4.5

In the adjacent figure,$\angle \mathrm{BAC} = 90°$ and $\mathrm{AD}\perp \mathrm{BC}$, then

Two poles of heights $6 \mathrm{m}$ and $11 \mathrm{m}$stand vertically on a plane ground. If the distance between their feet is$12 \mathrm{m}$, what is the distance between their tops?
 

In the given figure, $\mathrm{PR}=26 \mathrm{cm}, \mathrm{QR}=24 \mathrm{cm},$ $\angle \mathrm{PAQ}=90°$ , $\mathrm{PA}=6 \mathrm{cm}$ and $\mathrm{QA}=8 \mathrm{cm}$. Find $\angle \mathrm{PQR}$.

A tangent is perpendicular to the radius at the

How many tangents can be drawn to the circle from an exterior point?

The two tangents from an external points$\mathrm{P}$ to a circle with centre at $\mathrm{O}$ are $\mathrm{PA}$and $\mathrm{PB}$. If $\angle \mathrm{APB}=70°$then the value of$\angle \mathrm{AOB}$ is

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

In figure if $\mathrm{PR}$ is tangent to the circle at$\mathrm{P}$ and $\mathrm{O}$ is the centre of the circle, then$\angle \mathrm{POQ}$ is