How do we know the size of atoms in body centered cubic system? I'm told that in the normal cubic system there are $\frac18$ of an atom at each corner and these atoms' radius are such that $a = 2r$ ($a$ is the lattice constant, $r$ radius of an atom).

In bbc (body centered cubic system) they say the atoms in the diagonals are touching, and as a consequence the atoms at each corner are not big enough to satisfy the above relation $a = 2r$

Why is this? Couldn't it be like the normal cubic system but stick an atom in the center to fill up the remaining space? How do we know that they touch along the cube's diagonal and not along the edges?
The easiest answer in my opinion; try it! If each atom has the same radius, it is simply not possible to fit one of them into the center of the cubic system (known as a cubic hole). It is, however, possible if the atom is sufficiently small. CsCl is an example of such a compound. 

One can show this geometrically (as is done here), but you can also convince yourself that it must be the case using equally-sized tennis balls or something similar to try it out in practise.