Question

find the length of a tangent drawn to a circle with radius 3 cm from a point 4 cm from the center of the circle

Answer 1

Step-by-step explanation:

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

⇒PT2 =16

⇒PT= 16

⇒PT=4