Question 2
Suppose a regular pentagon $ABCDE$ is given. Let $F$ be the point of intersection of the lines $BE$ and $AC$. Suppose that a straight line going through $F$ intersects sides $AB$ and $CD$ at the points $G$, $H$, respectively, and $BG = 4$ and $CH = 5$ hold. Find the length of the line segment $AG$. Here by $XY$ we denote the length of the line segment $XY$ as well.
