Question

what is the measure of angle cab in circle o?

\\(24^\circ\\)
\\(48^\circ\\)
\\(72^\circ\\)
\\(96^\circ\\)

Explanation:

<pre_analysis>
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"new_concepts": [],
"current_concepts": [
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<reasoning>

Identify the given values and geometric relationships

\[

$$\begin{aligned} &\text{Central angle } \angle COB = 48^\circ \\ &\text{Inscribed angle } \angle CAB \text{ intercepts the same arc } \widehat{CB} \end{aligned}$$

\]

Apply the Inscribed Angle Theorem

\[

$$\begin{aligned} &m\angle CAB = \frac{1}{2} \cdot m\angle COB \\ &m\angle CAB = \frac{1}{2} \cdot 48^\circ = 24^\circ \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(24^\circ\)</mcq-correct>
<mcq-option>(B) \(48^\circ\)</mcq-option>
<mcq-option>(C) \(72^\circ\)</mcq-option>
<mcq-option>(D) \(96^\circ\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Inscribed Angle Theorem"
]
}
</post_analysis>

Answer:

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"new_concepts": [],
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</pre_analysis>

<reasoning>

Identify the given values and geometric relationships

\[

$$\begin{aligned} &\text{Central angle } \angle COB = 48^\circ \\ &\text{Inscribed angle } \angle CAB \text{ intercepts the same arc } \widehat{CB} \end{aligned}$$

\]

Apply the Inscribed Angle Theorem

\[

$$\begin{aligned} &m\angle CAB = \frac{1}{2} \cdot m\angle COB \\ &m\angle CAB = \frac{1}{2} \cdot 48^\circ = 24^\circ \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(24^\circ\)</mcq-correct>
<mcq-option>(B) \(48^\circ\)</mcq-option>
<mcq-option>(C) \(72^\circ\)</mcq-option>
<mcq-option>(D) \(96^\circ\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Inscribed Angle Theorem"
]
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</post_analysis>