5.2.4.5 Various problems on the plane

In a trapezoid \( A B C D \), with a large base \( A D= \) 24 and a side \( A B=12 \), an angle bisector \( \angle A \) is drawn, which intersects the side \( C D \) at the point \( M \) and the line \( B C \) at the point \( K \). \( A M=16, M K=4 \). Find the length of side \( C D \).