How can we measure the atomic radius of an atom?
As you told it is not possible to measure the inter nuclear distance of single atom. But here internuclear distance does not mean diameter of a single atom but it means distance between nucleus of two atom of same element. 

 

This internuclear distance can be determined by two methods:


X-rays method
Spectroscopy method




Note: Atomic radius is not a set value for a given atom. Eg. $\ce{Fe^{+2}}$ ion have different atomic radius than  $\ce{Fe+}$. Moreover,  $\ce{Fe^{+2}}$&lt;  $\ce{Fe+}$