You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>Gate AB in <image 1> is a quarter circle 10 ft wide into the paper and hinged at B . Find the force F just sufficient to keep the gate from opening. The gate is uniform and weighs 3000 lbf. 
A. F=7490lbf
B. F=7470lbf
C. F=7480lbf

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
C
Gate AB in <image 1> is a quarter circle 10 ft wide into the paper and hinged at B . Find the force F just sufficient to keep the gate from opening. The gate is uniform and weighs 3000 lbf. 
A. F=7490lbf
B. F=7470lbf
C. F=7480lbf

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
val