3. Point $M$ lies on the leg $A C$ of the right triangle $A B C$ with a right angle at $C$, such that $A M=2, M C=16$. Segment $M H$ is the altitude of triangle $A M B$. Point $D$ is located on the line $M H$ such that the angle $A D B$ is $90^{\circ}$, and points $C$ and $D$ lie on the same side of the line $A B$. Find the length of segment $B L$, if $L$ is the intersection of $B D$ and $A C$, and the tangent of angle $A C H$ is 1/18. (16 points)
Solution. 1. A circle can be circumscribed around quadrilateral $A B C D$ with diameter $A B$ (angles $A D B$ and $A C B$ are right angles). Then $\angle A B D=\angle A C D$,

$$
\angle H A D=90^{\circ}-\angle A B D, \angle A D H=\angle A B D=\angle A C D
$$

Triangles $A C D$ and $A D M$ are similar, and $\frac{A D}{A C}=\frac{A M}{A D}=$ $\frac{M D}{D C}, A D^{2}=A C \cdot A M=2 \cdot 18=36, A D=6$.