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2015-12-22T20:50:37+05:30
 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) 
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2015-12-22T20:56:23+05:30

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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,

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