Question

A point $P$ is $10cm$ from the centre of a circle. The length of the tangent drawn from $P$ to the circle is $8cm$. The radius of the circle is equal to

• A. $4cm$
• B. $5cm$
• C. $6cm$
• D. none of these

Answer 1

Answer: (C)

$6cm$

Given- $O$ is the centre of a circle to which a tangent $PT=8cm$ has been drawn to the circle at T when $OP=10cm$.
To find out- The radius of the given circle$=?$
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 radii 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 $OT=\sqrt{{OP}^2-{OT}^2}=\sqrt{{10}^2-8^2}cm=6cm.$
$\therefore$ The radius of the given circle$=6cm$.
Ans- Option-C