Four unit circles surround a smaller circle. Find the radius of the smaller circle.
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 =
So......the diameter of the small circle = 2√2 - 2 = 2 [ √2 - 1]
And its radius is 1/2 of this = [ √2 - 1 ] units
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,