This thesis presents various aspects of the study of a geometrical theorem that was published in 1858. by the English mathematician Hamnet Holditch. In his original formulation it yielded the area of a planar region limited by a closed curve C and the locus of the point dividing a chord of C into two segments of given lengths \( a\) and \(b\), when that chord moves (rotates) along the curve C. A surprising result that the area is simply equal to ab , not depending on the shape or the size of the curve C, provoked a considerable interest with mathematicians who attempted to discover a deeper reason to that statement. Such an investigation also involves finding precise assumptions for the theorem to be true as well as examination of possible generalizations and analogous results in three dimensions. An especially intriguing part of the theorem is played by a ”hidden” ellipse, whose area is readily apparent in the statement. In the final chapter it is briefly described a procedure of construction of a sequence of polygons, with their associated so-called Holditch curves converging to the desired ellipse.