To make the circle has an area of 4, as much as the square 2x2 in this picture below, what length of radius is needed?
It doesn't take a genius to figure that out.
The area of a circle is given by pi*r^2.
You want that equal to 4, so you want r=sqrt(4/pi)=1.1283791671...
AND at what angle does the intersection (circle line and square line) occur? (North=0°)
Again, doesn't take a genius.
Cos(a)=x/r (or as you have decided to take north to be 0=y/r).
Sticking in the numbers, that means:
a=acos(1/sqrt(4/pi))=27.5971126°
Any more of your very simple homework that you need doing?