Question

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

Answer 1

Answer

Draw a circle, taking C as centre and radius CT=3 cm

Let  

PT be the tangent, drawn from point P to the centre C

Then,  

CP=5 cm

CT=3 cm       (Given)

Now, ∠CTP=90  

o

    (since radius is perpendicular to tangent)

In right Δ CPT,

CP  2

=PT  2

+CT  2

     (By Pythagoras theorem)

⇒(5) 2

=PT  2

+(3)  2

 

⇒PT  2

=25−9

⇒PT  2  =16

⇒PT=  16

​  

 

⇒PT=4

Therefore, length of tangent =4 cm

Answer 2

Answer:

Draw a circle, taking C as centre and radius CT=3 cm

Let,

PT be the tangent, drawn from point P to the centre C

Then,

CP=5 cm

CT=3 cm (Given)

Now,

∠CTP=90°

(since radius is perpendicular to tangent)

In right ∆ CPT,

CP² = PT² + CT² (By Pythagoras theorem)

⇒(5)² = PT² + (3)²

⇒PT² = 25 − 9

⇒PT² = 16

⇒PT= √16

⇒PT=4

Therefore, length of tangent =4 cm