ÖMO 2004 Problem 3

A trapezoid $ABCD$ with perpendicular diagonals $AC$ and $BD$ is inscribed in a circle $k$ . Let $k_a$ and $k_c$ respectively be the circles with diameters $AB$ and $CD$ . Compute the area of the region which is inside the circle $k$ , but outside the circles $k_a$ and $k_c$ .