KöMaL 2014 A608

Suppose that the convex polygonal disks $P_1$, $P_2$ and $P_3$, lying in the plane, satisfy the property that for arbitrary points $A\in P_1$, $B\in P_2$ and $C\in P_3$, the area of the triangle $ABC$ is no more than a unit. Prove that there are two different ones among the disks $P_1$, $P_2$ and $P_3$ whose area is at most $8$ units in total.