1.39. A point $O$ inside a convex quadrilateral of area $S$ is reflected symmetrically with respect to the midpoints of its sides. Find the area of the quadrilateral with vertices at the resulting points.

## §4. Auxiliary Congruent Triangles

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1.39. Let $E, F, G$ and $H$ be the midpoints of the sides of quadrilateral $ABCD$; points $E_{1}, F_{1}, G_{1}$ and $H_{1}$ are symmetric to point $O$ with respect to these points. Since $EF$ is the midline of triangle $E_{1} O F_{1}$, then $S_{E_{1} O F_{1}}=4 S_{E O F}$. Similarly, $S_{F_{1} O G_{1}}=4 S_{F O G}, S_{G_{1} O H_{1}}=4 S_{G O H}$ and $S_{H_{1} O E_{1}}=4 S_{H O E}$. Therefore, $S_{E_{1} F_{1} G_{1} H_{1}}=4 S_{E F G H}$. According to problem 1.39, a) $S_{A B C D}=2 S_{E F G H}$. Therefore, $S_{E_{1} F_{1} G_{1} H_{1}}=2 S_{A B C D}=2 S$.