3.33. In the tetrahedron $A B C D$, 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 passing through the edge $A B$ and the center of the sphere inscribed in the tetrahedron.
3.33. Let $a=AB, x$ be the area of the desired section. Using the formula from problem 3.3 for the volume of tetrahedron $ABCD$ and its parts, we get

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

Therefore, $x=\frac{2 p q \cos (\alpha / 2)}{p+q}$.