MathNet 2010 — Part 07 Question 73

Triangle $A B C$ is given with $A B = 13$, $B C = 14$, $C A = 15$. Let $E$ and $F$ be the feet of the altitudes from $B$ and $C$, respectively. Let $G$ be the foot of the altitude from $A$ in triangle $A F E$. Find $A G$.