Solution

The fact that the circles meet at right angles is a red herring. The solution is trivial and does not take that fact into account:

Let X be the area of the intersection. Then the remaining portions of the two circles have the areas (π 20² - X) and (π 15² - X), with the difference

independent of X.

Indeed, it is not important that the two shapes be circles. The numerical answer will be the same for any two blobs of areas π 20² and π 15².