Variant 10.4.2. Given a parallelogram $A B C D$, point $M$ is the midpoint of side $B C$. On side $A D$, there is a point $K$ such that $B K = B M$ and quadrilateral $K B M D$ is cyclic.

(a) (2 points) What is the length of segment $M D$, if $A D = 19$?

(b) (2 points) How many degrees does angle $K M D$ measure, if $\angle B A D = 44^{\circ}$?

![](https://cdn.mathpix.com/cropped/2024_05_06_baaf26a33e2d9a36d9b4g-10.jpg?height=277&width=505&top_left_y=1468&top_left_x=468)
Answer: (a) 9.5. (b) 42.