  We consider a billiard in the punctured torus obtained by removing a small
disk from the two-dimensional flat torus, with trajectory starting from the
center of the puncture. In this case the phase space is given by the range of
the velocity only. We prove that the probability measures on $[0,\infty)$
associated with the first exit time are weakly convergent when the size of the
puncture tends to zero and explicitly compute the density of the limit.
