13. (GDR 1) Find whether among all quadrilaterals whose interiors lie inside a semicircle of radius \( r \) there exists one (or more) with maximal area. If so, determine their shape and area.
13. The maximum area is $3 \sqrt{3} r^{2} / 4$ (where $r$ is the radius of the semicircle) and is attained in the case of a trapezoid with two vertices at the endpoints of the diameter of the semicircle and the other two vertices dividing the semicircle into three equal arcs.