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: <image1>

In this diagram semi-circles are constructed on diameters $\overline{AB}$, $\overline{AC}$, and $\overline{CB}$, so that they are mutually tangent.  If $\overline{CD} \bot \overline{AB}$, then the ratio of the shaded area to the area of a circle with $\overline{CD}$ as radius is:
Choices:
(A) $1:2$
(B) $1:3$
(C) $\sqrt{3}:7$
(D) $1:4$
(E) $\sqrt{2}:6$ 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
D
Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: <image1>

In this diagram semi-circles are constructed on diameters $\overline{AB}$, $\overline{AC}$, and $\overline{CB}$, so that they are mutually tangent.  If $\overline{CD} \bot \overline{AB}$, then the ratio of the shaded area to the area of a circle with $\overline{CD}$ as radius is:
Choices:
(A) $1:2$
(B) $1:3$
(C) $\sqrt{3}:7$
(D) $1:4$
(E) $\sqrt{2}:6$ 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