MathNet 2019-part-01 — 184 problems (EN–VI) Question 115

The squares $AA_1DE$ and $AA_1FG$ are constructed on the bisector $AA_1$ of the non-isosceles triangle $ABC$ such that the points $B$ and $F$ lie in different half-planes with respect to the line $AA_1$.
Prove that the lines $BD$, $CF$ and $EG$ are concurrent.