A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Consider triangle ABC with coordinates A=(5, -8), B=(-4, -2), and C=(9, 9). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.
Assistant: Let me solve this step by step.
<think>
user