Question 172
In an acute triangle $ABC$, point $H$ is the intersection point of altitude $CE$ to $AB$ and altitude $BD$ to $AC$. A circle with $DE$ as its diameter intersects $AB$ and $AC$ at points $F$ and $G$, respectively. $FG$ and $AH$ intersect at point $K$. If $BC = 25$, $BD = 20$, and $BE = 7$, find the length of $AK$.