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Answer :
In geometry, the term used to describe an angle whose vertex is at the center of a circle and whose sides are radii of the circle is known as a central angle. Therefore, the correct choice is option B: central angle.
Explanation
Central Angle:
- A central angle is formed when two radii of a circle create an angle at the circle's center. This angle is crucial as it defines a sector of the circle. The size of the central angle determines the fraction of the circle's circumference or area that it encloses.
Intercepted Angle:
- This is not a standard term for the specific angle described in this context, so it does not apply here.
Inscribed Angle:
- An inscribed angle is formed anywhere on the circle such that its vertex lies on the circle and its sides contain chords of the circle. This is different from a central angle whose vertex is at the center.
Circumscribed Angle:
- A circumscribed angle is formed outside the circle, typically where two tangent lines intersect outside the circle. This is unlike the central angle.
Key Points
- Vertex Location: The vertex of a central angle is precisely at the circle's center.
- Importance: Central angles are often used in circle theorems and calculating arc lengths and sectors.
- Real-World Application: Understanding central angles is useful in fields such as engineering, architecture, and even navigation.
By understanding these definitions and properties, students can accurately identify and use central angles in various mathematical problems and real-world applications.
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