Question

Find the length of the tangent to a circle with radius $5$ cm, from a point at a distance of $13$ cm from the center.

• A. $12$ cm
• B. $24$ cm
• C. $18$ cm
• D. $35$ cm

Answer 1

The correct option is A $12$ cm

We join OT which is a radius .

$\therefore$ OT $=5$ cm.

Now $\angle OAT={90}^o$ since the angle between a tangent to a circle and the radius joining the centre and the point of contact $={90}^o$.

$\therefore \Delta$ OAT is a right one with OA as hypotenuse.

So, applying Pythagoras theorem, we have AT$=\sqrt{{OA}^2-{OT}^2}=\sqrt{{13}^2-5^2}$ cm$=12$cm.

Ans- Option A.