33. On the diagonal $AC$ of the convex quadrilateral $ABCD$, there is the center of a circle of radius $r$, which is tangent to the sides $AB, AD$, and $BC$. On the diagonal $BD$, there is the center of a circle of the same radius $r$, which is tangent to the sides $BC, CD$, and $AD$. Find the area of the quadrilateral $ABCD$, given that the specified circles touch each other externally.
33. From the condition, it follows that $A B C D$ is a trapezoid ($B C \| A D$), $A C$ is the bisector of angle $B A D$; therefore, $|A B|=|B C|$; similarly, $|B C|=|C D|$. Let $|A B|=|B C|=|C D|=a,|A D|=b$. The distance between the midpoints of the diagonals is $2 r$, hence, $\frac{b-a}{2}=2 r$. Draw the height $B M$ from point $B$ to $A D$,

$$
|A M|=\frac{b-a}{2}=2 r, \quad|B M|=2 r
$$

Therefore, $a=|A B|=2 r \sqrt{2}, b=4 r+2 r \sqrt{2}$.

Answer: $S=4 r^{2}(\sqrt{2}+1)$.