The invariant distribution of a sequence of random collinear triangle shapes

The shape of the nth in a sequence of random triangle shapes is (xn, yn). It was shown in [8] and [9] that yn . 0, almost surely, as n . .. In this paper we show that x. converges in distribution, as n.., to a random variable x, and we find the probability distribution of x. The convergence in law of xn enables us to complete an argument used in one part of [9].