The two tangents together with the two radii and the line joining the intersection of the tangents with the centre of the circle form congruent right angled triangles. 
For each triangle, the angle between the intersection line and the the tangent is 30°. 
Then, tan 30 = 3/L....where L is the required length. 
L = 3/tan 30 = 3/(1/√3) = 3√3 

answer : 
3*(root of 3) 
  • qais
  • Content Quality

This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let the radius be r units
Length of tangent = L
as we know that, tangent makes 90° with the radius.
tan 30° = r/L
⇒L = r/tan30°
      =r√3 units
refer the diagram below,