Question

In the ddjoining figure $O$ is the centre of the circle. Forom point $RsegRM$ and $segRN$ are tengent segment touching the circle at $M$ and $N$. If $\left(OR\right)=10cm$ and radius of the circle $=5cm$, then
What is the length of each tangent segment?

Answer 1

It is given that segment $RM$ and segment $RN$ are tanget segments touching the circle at $M$ and $N$, respectively.

$\therefore \angle OMR=\angle ONR={90}^{\circ }$(Tangent at any point of a circle is perpendicular to the radius through out the point of contact.)

$OM=5$cm and $OR=10$cm

In right angled $△OMR$

${OR}^2={OM}^2+{MR}^2$

$\Rightarrow MR=\sqrt{{OR}^2-{OM}^2}=\sqrt{{10}^2-5^2}=\sqrt{100-25}=\sqrt{75}=5\sqrt{3}$cm

Tangent segments drawn from an external point to a circle are congruent.

$\therefore MR=NR=5\sqrt{3}$cms