Question 171
Let $ABCD$ be a square and $E$ a point on side $CD$. The circle inscribed in triangle $ADE$ touches $DE$ at $F$, and the circle inside quadrilateral $ABCE$, tangent to sides $AB$, $BC$, $EA$, touches $AB$ at $G$. Prove that lines $AE$, $BD$, and $FG$ meet in a point.