Question
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Is this statement true or false? The vertex of a central angle must be at the center of the circle.

Ask by Alexander Peterson. in the United States
Jan 23,2025

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Answer

The vertex of a central angle is at the center of the circle.

Solution

The statement is true. In a circle, a central angle is defined as an angle whose vertex is located at the center of the circle, and its sides (or rays) extend to the circumference of the circle. Therefore, the vertex of a central angle must indeed be at the center of the circle.

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Extra Insights

True! In fact, a central angle is formed by two radii of the circle, and its vertex is indeed at the circle's center. Picture this: when you slice a pizza, the point where the slices converge is at the center, creating that delicious central angle, and each slice represents a different fraction of the whole circle. Additionally, this property is super useful in real-world applications! When designing anything circular, like clock faces or roundabouts, knowing that the vertex of each central angle sits in the center helps in accurately dividing those areas into equal sections, ensuring proper spacing and visual symmetry that are both functional and aesthetically pleasing.

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