## Similar triangles (other). $\quad[$ [Ratio of areas of triangles with a common base or common height] $]$ Difficult [The area of a figure is equal to the sum of the areas of the figures into which it is divided Cauchy's inequality

The diagonals of a convex quadrilateral $ABCD$ intersect at point $E$. It is known that the area of each of the triangles $ABE$ and $DCE$ is 1, the area of the entire quadrilateral does not exceed 4, and $AD=3$. Find the side $BC$.

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