4. Given the circle $\Gamma: x^{2}+y^{2}=1$ intersects the $x$-axis at points $A$ and $B$ (from left to right), $P$ is a moving point on the circle $\Gamma$, $l$ is a line passing through point $P$ and tangent to the circle $\Gamma$, and a perpendicular line is drawn from point $A$ to $l$ intersecting the line $B P$ at point $M$. Then the maximum value of the distance from point $M$ to the line $x+2 y-9=0$ is $\qquad$
4. $2 \sqrt{5}+2$.

It is easy to know that $M A=2$.
Therefore, the locus of point $M$ is the circle $(x+1)^{2}+y^{2}=4$, and the distance from the center of the circle to the line $x+2 y-9=0$ is $\frac{10}{\sqrt{5}}=2 \sqrt{5}$.

Thus, the maximum distance from point $M$ to the line $x+2 y-9=0$ is $2 \sqrt{5}+2$.