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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Tangent-Chord Theorem", "Arc Measure" ], "new_concepts": [], "current_concepts": [ "Tangent-Chord Theorem", "Arc Measure" ] } ## Identify the given angle and geometric relationship $$ \begin{aligned} &\text{Line } EF \text{ is tangent to circle } G \text{ at point } A.\ &\text{Chord } AC \text{ and tangent line } EF \text{ form angle } \angle CAE.\ &\angle CAE = 95^\circ \quad (\text{indicated by the angle arc at } A) \end{aligned} $$ ## Apply the Tangent-Chord Theorem $$ \begin{aligned} &\text{m}\widehat{CBA} = 2 \cdot \angle CAE\ &\text{m}\widehat{CBA} = 2 \cdot 95^\circ = 190^\circ \end{aligned} $$

90°

95°

190°

195°

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Tangent-Chord Theorem" ] }

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Question

Explanation:

Identify the given angle and geometric relationship

Apply the Tangent-Chord Theorem

Answer: