Geometry

Find the radius of the circle.

$(1+r)^2=(\dfrac{\overline{AC}}{2}-r)^2+1^2\\ (1+r)^2=(\dfrac{4}{2}-r)^2+1^2\\ 1+2r+r^2=4-4r+r^2+1\\ 6r=4\\ \color{blue}r=\dfrac{2}{3}$

The radius of the circle is $\color{blue}\frac{2}{3}\ .$

  !