<Tri-2025-2225>, hint

On line BC, MD extended intersect line BC at E.

Draw a line , parallel to MDE, cutting line BCE at F.

Triangles DCE and ACF are similar, Line BD cut AF at G, midpoint of AF

(Triangle BDM and BDE are congruent and BM=MA--> BD=DG, MA=EF)

AB=BF=BC+CE+EF--->DE=1/2 GF-->CE=1/4CF-->CE=1/4(CE+AB/2)--->CE=AB/6. BF=AB=BC+CE+EF=BC+AB/6+AB/2---> AB=3BC.