Correct Answer - Option 3 : r/√3

__Concept:__

The tangent length of the curve is given by,

\({\rm{T}} = {\rm{R}}\tan \frac{{\rm{Δ }}}{2}{\rm{\;}}\)

Where,

Δ = Deviation or deflection angle in degrees

Δ = 180° - Angle of intersection

R = Radius of curve in m

**Calculation:**

Given,

R = r, Δ = 60°

\({\rm{T}} = {\rm{R}}\tan \frac{{\rm{Δ }}}{2}{\rm{\;}}\)

\({\rm{T}} = {\rm{r}} \times \tan \frac{{\rm{60 }}}{2}{\rm{\;}}\)

\({\rm{T}} = {\rm{r}} \times \tan {{\rm{30 }}}{}{\rm{\;}}\)

\({\rm{T}} = {\rm{}}\frac{{\rm{r }}}{\sqrt3}{\rm{\;}}\)