Question

find the length of tangent drawn to a circle with radius 7cm from a point 25 cm away from the centre

Answer 1

the length of the tangent
=root(25^2-7^2)
=root(625-49)
=root(575)
=24 cm

Answer 2

Given:

Radius=7cm

Distance of the point from center=25cm

To find:

The length of the tangent

Solution:

The required length is 24 cm.

We can obtain the length by using the Pythagoras theorem.

Let the tangent be AB.

Since the tangent and the radius are perpendicular to each other, we get the following.

$OB^{2} +AB^{2} =OA^{2}$

Now, we know that OA=25cm and OB=7cm.

Using the values,

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

$AB^{2}$=625-49

AB=$\sqrt{576}$

AB=24 cm

Therefore, the required length is 24 cm.