5.2.4.5 Various Problems on the Plane

In the trapezoid \ (a b c d \), with a large base \ (a d = \) 24 and the side \ (a b = 12 \), a bisector of the angle \ (\ angle a \) was drawn, which crosses the side \ (C D \) at point \ (m \) a straight \ (b c \) at point \ (k \). \ (A m = 16, m k = 4 \). Find the length of the side \ (C D \).