72. In the triangular pyramid $A B C D$, the faces $A B C$ and $A B D$ have areas $p$ and $q$ and form an angle $\alpha$ between them. Find the area of the section of the pyramid passing through the edge $A B$ and the center of the sphere inscribed in the pyramid.
72. If $x$ is the area of the desired section, $|A B|=a$, 10, using the formula for the volume of the pyramid $A B C D$ and its parts from problem 11, we get

$$
\frac{2}{3} \frac{p x \sin \frac{\alpha}{2}}{a}+\frac{2}{3} \frac{q x \sin \frac{\alpha}{2}}{a}=\frac{2}{3} \frac{p q \sin \alpha}{a}
$$

from which

$$
x=\frac{2 p q \cos \frac{\alpha}{2}}{p+q}
$$