  A disc packing in the plane is compact if its contact graph is a
triangulation. There are $9$ values of $r$ such that a compact packing by discs
of radii $1$ and $r$ exists. We prove, for each of these $9$ values, that the
maximal density over all the packings by discs of radii $1$ and $r$ is reached
for a compact packing (we give it as well as its density).
