<|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
 The mutually perpendicular diameter \( KM \) and chord \( AB \) of a given circle intersect at point \( N \), where \( KN \neq NM \). Point \( L \) is taken on the extension of segment \( AB \) beyond point \( A \), such that \( LN = a \) and \( AN = b \). Find the distance from point \( N \) to the orthocenter of triangle \( KLM \). 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
0
The mutually perpendicular diameter \( KM \) and chord \( AB \) of a given circle intersect at point \( N \), where \( KN \neq NM \). Point \( L \) is taken on the extension of segment \( AB \) beyond point \( A \), such that \( LN = a \) and \( AN = b \). Find the distance from point \( N \) to the orthocenter of triangle \( KLM \).
test