24. In triangle $ABC$, a point $M$ is taken on side $AC$, and a point $N$ is taken on side $BC$. Segments $AN$ and $BM$ intersect at point $O$. Find the area of triangle $CMN$, if the areas of triangles $OMA$, $OAB$, and $OBM$ are $S_{1}$, $S_{2}$, and $S_{3}$, respectively.
24. If $x$ is the area of triangle $O M N$, and $y$ is the area of triangle $C M N$, then

$\frac{|O N|}{|O A|}=\frac{x}{S_{1}}=\frac{S_{3}}{S_{2}}, \quad x=\frac{S_{1} S_{3}}{S_{2}}, \quad \frac{|A M|}{|M C|}=\frac{S_{1}+x}{y}=\frac{S_{1}+S_{2}}{S_{3}+x+y}$, from which $y=\frac{S_{1} S_{3}\left(S_{1}+S_{2}\right)\left(S_{3}+S_{2}\right)}{S_{2}\left(S_{2}^{2}-S_{1} S_{3}\right)}$.