Question

find the length of the tangent drawn to a circle with radius 3 cm from a point 5 cm from the centre of the circle
​

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.