you still need the 2 angles "a" and "b", but then you only have an equality.
That equation doesn't give you either angle.
There is an easy way to solve this, since the triangle from
one point of intersection of the circles to both centres has sides 3, 4 and 5.
This is right-angled since
Then, the angle "a" you mentioned is
Also "b" is etc.
Now draw the chord and work with the back to back right-angled triangles.
Now that you have the angles, you can calculate the overlapping area
by subtracting the triangle within the circle from the sector,
doing that for both circles and adding the two results.
Then double that to include the part underneath the line joining the circle centres.