Question

A point $P$ is $26cm$ away from the center $O$ of a circle and the length $PT$ of the tangent drawn from $P$ to the circle is $10cm$. Find the radius of the circle.

• A. $24cm$
• B. $14cm$
• C. $20cm$
• D. $4cm$

Answer 1

The correct option is A $24cm$

Length of tangent $l=\sqrt{d^2-r^2}$

Here, $d=26cm,l=10cm$

$\therefore 10=\sqrt{{26}^2-r^2}$

$10=\sqrt{676-r^2}$

by squaring on both sides, we get

$100=676-r^2$

$r^2=676-100=576={24}^2$

$r=24cm$

The radius of the circle $=24cm.$