Hi
Dont know whether the solution is correct or not.But i think if we draw a circle and then inscribe a triangle say ABC.
Then draw a tangent to the circle at point B say DBE.

Now if the chord starting from point B has to be greater than the side of the Triangle ABC it has to lie in between angle ABC=60 degrees.

So, the probablity (of chord > side of triangle ABC)< 60/180=1/3

Comments are welcome.

regards