HMMT 2025 G8

Let $A B C D$ be an isosceles trapezoid such that $C D > A B = 4$ . Let $E$ be a point on line $C D$ such that $D E = 2$ and $D$ lies between $E$ and $C$ . Let $M$ be the midpoint of $\overline{{A E}}$ . Given that points $A$ , $B$ , $C$ , $D$ , and $M$ lie on a circle with radius 5, compute $M D$ .