Question

A tangent is drawn to a circle from a point $P$ which is at a distance of $13$ cm from the center of the circle of radius $5cm.$ The length of the tangent is?

• A. $10cm$
• B. $12cm$
• C. $18cm$
• D. None of the options

Answer 1

Answer: (B)

$12cm$

Given-

O is the centre of a circle of $radius=OT=OR=5cm$. PT is the tangent to the circle from P at T. OP=13cm. To find out- PT=?

Solution-

$\angle OTP={90}^o$ since the tangent to a circle makes ${90}^o$ angle with the radius at the point of contact.

$\therefore \Delta OTP$ is a right one with OP as the hypotenuse.

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

Thus the correct answer is $12cm$