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>Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: A circle $K$ is inscribed in a quarter circle with radius 6 as shown in the figure. What is the radius of circle $K$?
<image1>
Choices:
(A) $\frac{6-\sqrt{2}}{2}$
(B) $\frac{3 \sqrt{2}}{2}$
(C) 2.5
(D) 3
(E) $6(\sqrt{2}-1)$ 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
E
Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: A circle $K$ is inscribed in a quarter circle with radius 6 as shown in the figure. What is the radius of circle $K$?
<image1>
Choices:
(A) $\frac{6-\sqrt{2}}{2}$
(B) $\frac{3 \sqrt{2}}{2}$
(C) 2.5
(D) 3
(E) $6(\sqrt{2}-1)$ 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