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Considering edge cases gets you 40\% of the points. These include: no area and one circle within the other.
The intersection of two circles can be seen as two chords. The area of a chord can be found by subtracting the area of a triangle by the area of the inner isosceles triangle.
To make the problem simpler, translate the two circles onto the x-axis. One of which has a center on the origin. To do this, find the distance d between the two centers. Now the new centers are (0, 0) and (d, 0). Then solve for the points of intersection. Now you have all the pieces of information you need to find the areas.
Read the problem.