Question 23
Altitudes $B E$ and $C F$ of acute triangle $A B C$ intersect at $H$. Suppose that the altitudes of triangle $E H F$ concur on line $B C$. If $A B = 3$ and $A C = 4$, then $B C^{2} = \frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $100 a + b$.