What is a central angle?

A central angle is specifically defined as an angle whose vertex is located at the center of a circle, and its sides (or rays) extend to the circumference of the circle. This means that the two rays (or lines) that create the angle essentially connect the center point of the circle to two points on the circle itself. This geometric configuration is crucial for understanding various properties related to circles, such as the relationship between central angles and the arcs they subtend.

In the context of a circle, the central angle can help determine the magnitude of the arc length it subtends and is fundamental to the study of circle theorems. This concept becomes important not just in theoretical mathematics but also in practical applications such as engineering and physics, where the properties of circles often come into play.

Understanding the definition of a central angle is essential, especially when dealing with circle-related problems and the relationships that exist between angles and arcs in circle geometry.