  We consider circle packings in the plane with circles of sizes $1$, $r\simeq
0.834$ and $s\simeq 0.651$. These sizes are algebraic numbers which allow a
compact packing, that is, a packing in which each hole is formed by three
mutually tangent circles. Compact packings are believed to maximize the density
when there are possible. We prove that it is indeed the case for these sizes.
The proof should be generalizable to other sizes which allow compact packings
and is a first step towards a general result.
