Knowing the areas of the circles, you know their radii. If one of the circles does not touch the others, it is trivial.
If no circle is fully contained in another one , you can find the distances between each of the centerpoints from their intersecting area and you have all data you need.
If one circle is fully contained and the two others are intersecting, you can ignore the outer circle and the problem is trivial.
If two circles are contained in one circle, the problem is trivial too.