Question

From a point $Q$, the length of the tangent to a circle is $24$ cm and the distance of $Q$ from the centre is $25$ cm. The radius of the circle is-

• A. $7$ cm
• B. $12$ cm
• C. $15$ cm
• D. $24.5$ cm

Answer 1

The correct option is A $7$ cm

Given:-

Tangent $=XY$

Point of contact $=B$

Length of tangent to the circle, $PQ=24cm$

And $OQ=24cm$

Sol:-

Since $XY$ is tangent,

$OP\perp XY(\because \text{Tangent at any point of circle is perpendicular to the radius through point of contact})$

$\therefore \angle OPQ=90$

Therefore, $△OPQ$ is a right angled triangle,

Using Pythagoras theorem,

${OQ}^2={OP}^2+{PQ}^2$

${\left(25\right)}^2={OP}^2+{\left(24\right)}^2$

$\Rightarrow OP=\sqrt{625-576}=7cm$

Hence radius of the circle is $7cm$.