Question

Find the length of the tangent drawn to a circle of radius $3$ cm, from a point at a distance $5$ cm from the center.

Answer 1

Draw a circle, taking $C$ as centre and radius $CT=3$ cm

Let

$PT$ be the tangent, drawn from point $P$ to the centre $C$

Then,

$CP=5$ cm

$CT=3$ cm (Given)

Now, $\angle CTP={90}^o$ (since radius is perpendicular to tangent)

In right $\Delta$ CPT,

$C{P}^2=P{T}^2+C{T}^2$ (By Pythagoras theorem)

$\Rightarrow (5{)}^2=P{T}^2+(3{)}^2$

$\Rightarrow P{T}^2=25-9$

$\Rightarrow P{T}^2=16$

$\Rightarrow PT=\sqrt{16}$

$\Rightarrow PT=4$

Therefore, length of tangent $=4$ cm.