Two circles of equal radii have following properties:

$\left(\mathrm{i}\right)$ They intersect each other orthogonally 

$\left(\mathrm{ii}\right)$ They touch both the curves $4\left(y+2\right)=x^2$ and $4\left(2-y\right)=x^2$ in the region that lies inside the two curves

Then the radius of the circles are