Question

A point $P$ is $25cm$ from the centre of a circle. The radius of the circle is $7cm$ and length of the tangent drawn from $P$ to the circle is $x$ cm. The value of $x=$ is

• A. $20cm$
• B. $24cm$
• C. $18cm$
• D. $12cm$

Answer 1

Answer: (B)

$24cm$

Given- $O$ is the centre of a circle to which a tangent $PT=x$ has been drawn to the circle at $T$ when $OP=25cm$. The radius of the given circle$=7cm$
To find out: $x=?$
Solution- We join $OT$.
$\therefore OT$ is a radius of the circle through the point of contact $T$ of the tangent $PT$. We know that the radius through the point of contact of a tangent to a circle is perpendicular to the tangent.
$\therefore OT\perp PT⟹\angle OTP={90}^o$.
$\therefore \Delta OTP$ is a right one with $OP$ as hypotenuse. So, applying Pythagoras theorem, we get
$PT=\sqrt{{OP}^2-{OT}^2}=\sqrt{{25}^2-7^2}cm=24cm$.
$\therefore$ The tangent to the given circle $PT=24cm$.
Ans- Option-B.