## Task 4 - 020734

Given a triangle $A B C$ with area $F_{1}$. Connect point $A$ with the midpoint $E$ of side $a$ and extend the segment beyond $E$ by itself. The endpoint is $D$; the area of triangle $A D C$ is $F_{2}$.

Calculate the ratio $F_{1}: F_{2}$!
When performing the construction, it is found that triangles $A C E$ and $B D E$ are congruent.

Indeed, $B E=C E$ ($E$ is the midpoint of $a$), $A E=E D$ (extension of $A E$ by itself), and $\angle A E C=\angle D E B$ (vertical angles). Thus, the two triangles are equal in area; by adding the area of triangle $A B E$, it follows that $F_{1}: F_{2}=1$.