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.

Time complexity

$\mathcal{O}(1)$

Problem

Read the problem.