Since the area of the square is 16 square units, each side of the 
square is the square root of 16 or 4 units.

This green line: 



is also 4 units and goes across both circles on the left.
so each of the four larger circles has radius 1.

Now let's draw a diagonal of the square and letter some points:




ABC is a right triangle,

AB=1, BC=1, so by the Pythagorean theorem AC = 

and since GH = AC, GH = 

CD and FG are both radii of the larger circles so they are 1 each.

Triangle AIH is a right triangle, AI = 4, IH = 4, so by the
Pythagorean theorem, diagonal AH = 

We add up the parts of the diagonal AH and equate the sum to  

AC + CD + DF + FG + GH =  

Substituting the values for the parts that we know the lengths of:

+1+DF+1+ = 

Now we solve for DF

+2+DF = 

DF =  

DF is the diameter of small circle E, so its radius

is  or  



Edwin