help

Find the centers of each of the 4  larger circles and connect them

This will form a square of 2 units on each side

And the distance from the center  of the circle at the top left to the  center of the circle on the bottom right  =

2√2  units

So......the diameter of the small circle =  2√2 - 2   = 2 [ √2 - 1]

And its radius is 1/2 of this  = [ √2 - 1 ]  units 

Hi wiseowl!

Connect the centers like in the following diagram: https://imgur.com/WoRzy2n

This forms a right triangle with equal legs of 2 units. 

The hypotenuse is equal to the diameter of the smaller circle plus 2. 

We can right the equation: \(2^2+ 2^2=(2+2x)^2\\ 8=4+8x+4x^2\\ x^2+2x-1=0\) 

Solving for x, we get x = √2 - 1

I hope this helped,

Gavin