<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Altitudes \( BE \) and \( CF \) of acute triangle \( ABC \) intersect at \( H \). Suppose that the altitudes of triangle \( EHF \) concur on line \( BC \). If \( AB=3 \) and \( AC=4 \), then \( BC^2=\frac{a}{b} \), where \(a\) and \(b\) are relatively prime positive integers. Compute \(100a+b\). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
33725
Altitudes \( BE \) and \( CF \) of acute triangle \( ABC \) intersect at \( H \). Suppose that the altitudes of triangle \( EHF \) concur on line \( BC \). If \( AB=3 \) and \( AC=4 \), then \( BC^2=\frac{a}{b} \), where \(a\) and \(b\) are relatively prime positive integers. Compute \(100a+b\).
test