Question

Find the length of the tangent drawn from a point whose distance from the centre of circle is 25 cm. Given that the radius of the circle is 7 cm.

• A. 20cm
• B. 24cm
• C. 28cm
• D. 30cm

Answer 1

The correct option is B

24cm

Since tangent at a point on the circle is perpendicular to the radius through the point.

$\therefore \angle OTP={90}^{\circ }$

In right angled triangle OTP

${OP}^2={OT}^2+{PT}^2$ (By Pythagoras theorem)

${25}^2=7^2+{PT}^2$

$625=49+{PT}^2$

${PT}^2=625-49=576$

$PT=\sqrt{576}=24$

Hence, length of tangent PT = 24 cm.