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*

    (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= $\sqrt{16}$

​⇒PT=4