Ex. 109. Two non-intersecting circles with centers at points $A$ and $B$ are inscribed in an angle of measure $\alpha\left(0<\alpha<180^{\circ}\right)$. The length of $A B$ is $n$. The segment $M N$ with endpoints on the sides of the angle is tangent to both circles. Find the difference in the areas of triangles $B M N$ and $A M N$.
Ex. 109. $\frac{n^{2} \sin \alpha}{4}$.