USAMO 1975 Problem 4

Two circles intersect at two points, one of them $\mathrm{X}$. Find $\mathrm{Y}$ on one circle and $\mathrm{Z}$ on the other, so that $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ are collinear and $\mathrm{XY} . \mathrm{XZ}$ is as large as possible.