Problem

Source:

Tags: geometry, construction



The student drew a triangle $ABC$ on the board, in which $AB>BC$. On the side $AB$ is taken point $D$ such that $BD = AC$. Let points $E$ and $F$ be the midpoints of the segments $AD$ and $BC$ respectively. Then the whole picture was erased, leaving only dots $E$ and $F$. Restore triangle $ABC$.