JMO 1994 Problem 2

Five points, no three collinear, are given on the plane. Let $l_1,l_2,\ldots ,l_{10}$ be the lengths of the ten segments joining any two of the given points. Prove that if $l_1^2,\ldots ,l_9^2$ are rational numbers, then $l_{10}^2$ is also a rational number.