Question

The length of a tangent from a point A at distance $5$ cm from the centre of circle is $4$ cm. The radius of the circle is

• A. $1$ cm
• B. $2$ cm
• C. $3$ cm
• D. $4$ cm

Answer 1

Answer: (C)

$3$ cm

Let $AT$ be the tangent drawn from a point $A$ to a circle with centre $O$ and $OA=5$ cm and $AT=4$ cm. Since tangent at a point is $\perp$ to the radius through the point of constant.
$\therefore OT\perp AT$
$\therefore$ from right $△OAT$,
$(OA{)}^2=(OT{)}^2+(TA{)}^2$
$\Rightarrow (5{)}^2=(OT{)}^2+(4{)}^2$
$\Rightarrow 25-16=(OT{)}^2$
$\Rightarrow 9=(OT{)}^2=OT=3$ cm
$\therefore$ radius of the circle $=3$ cm