Question 20
In the diagram, $ABCD$ is a square and $H$ is the intersection of its diagonals. Points $B,E,F,G$ are collinear, with $G$ on $AD$ and $E$ on $AC$. Also, $AF$ bisects $\angle CAD$, and $\angle AFB=90^\circ$. If $EH=13\sqrt2$, find $AG$.
Answer format: enter the integer answer without units. Leading zeros are optional; the original paper uses four-digit boxes.
Answer format: enter the integer answer without units. Leading zeros are optional; the original paper uses four-digit boxes.