Let $A D$ and $B C$ be two vertical poles at $A$ and $B$ respectively on a horizontal ground. If $A D=8 m, B C=11 m$ and $A B=10 m$; then the distance (in meters) of a point $M$ on $A B$ from the point $A$ such that $\mathrm{MD}^2+\mathrm{MC}^2$ is minimum is $\_\_\_\_$ .
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