A thin loop of a thread floats on a soap film formed inside a wire frame which is kept horizontal. When the film is pierced, the loop arranges in the form of a circle of radius r. If $\sigma$ is the surface tension of the soap solution, the tension in the wire will be 

Assume a small portion subtending an angle of $\theta$(very small angle) at the center. 

The force due to surface tension will be $2\sigma R\theta$( as the force is applied form both the surfaces)

The resultant of tension acing will be $2T\sin \left(\frac{\theta }{2}\right)\approx T\theta$

As the thread is in equilibrium $T\theta =2\sigma R\theta \Rightarrow T=2\sigma R$