Find whether among all quadrilaterals, whose interiors lie inside a semi-circle of radius , there exist one (or more) with maximum area. If so, determine their shape and area.
%V0
Find whether among all quadrilaterals, whose interiors lie inside a semi-circle of radius $r$, there exist one (or more) with maximum area. If so, determine their shape and area.
Izvor: Međunarodna matematička olimpijada, shortlist 1967
Školjka 
, there exist one (or more) with maximum area. If so, determine their shape and area.