5.2.4.3 Various Problems on the Plane

In a rectangular trapezoid \ (a b c d \ angle a \) a straight line, a large base \ (a d = 4 \), the side side \ (a b = 6 \), the bisector of the angle \ (\ angle d \) passes through the middle of the side \ (a b \). Calculate the length of the base \ (b c \).