Question

find the length of the tangent drawn to a circle of radius 3cm ,from a point at a distance 5cm from the centre

Answer 1

We know tangent to a radius of the circle is perpendicular
So, angle OAB=90degree
So by pythagoras theorem,
OB square=OAsquare+ABsquare

Answer 2

Answer:

The length of the tangent is 4cm.

Step-by-step explanation:

Given : The tangent drawn to a circle of radius 3cm ,from a point at a distance 5cm from the center.

To find : The length of the tangent?

Solution :

We draw a circle with center O and radius OA=3 cm and one tangent is form from the center forming a triangle OAB , OB=5 cm

Refer the attached figure below.

We know that, tangent to a radius of the circle is perpendicular  

So, ∠OAB=90°

Applying Pythagoras theorem in right angle triangle OAB,

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

$5^2=3^2+AB^2$

$25=9+AB^2$

$25-9=AB^2$

$\sqrt{16}=AB$

$AB=4$

Therefore, The length of the tangent is 4cm.