12.3.2.4 Geometric

condition: On the diameter of the CM of a circle of radius \( R \), a point \( A \) is selected, distant from the center of the circle at a distance \( a \in[0 ; R) \). Draw a chord \( L N \) through the point \( A \) so that the area of ​​the quadrilateral \( K L M N \) is maximum. Find this area.