The paper proves the following result: Consider a circle and a right triangle \(ABC\) such that \(AB\) is a diameter of the circle. Draw semicircles with diameters \(AC\) and \(BC\). Each of this semicircles, together with the original circle determines a lune. The sum of the areas of these lunes equals the area of the triangle \(ABC\).
The result is elementary and not very surprising, Nevertheless it can be a nice excercise for secondary school students and it is suitable to be worked out with GeoGebra.