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>In the diagram below, $\overline{P S}$ is a tangent to circle $O$ at point $S, \overline{P Q R}$ is a secant, $P S=x, P Q=3$, and $P R=x+18$.<image 1>What is the length of $\overline{P S}$ ?
A. 6
B. 9
C. 3
D. 27

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
B
In the diagram below, $\overline{P S}$ is a tangent to circle $O$ at point $S, \overline{P Q R}$ is a secant, $P S=x, P Q=3$, and $P R=x+18$.<image 1>What is the length of $\overline{P S}$ ?
A. 6
B. 9
C. 3
D. 27

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