Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is a central angle in relation to a circle?

1. An angle formed by two chords

2. An angle formed by a radius and a tangent

3. An angle whose vertex is at the center of the circle

4. An angle measured outside the circle

The correct answer is: An angle whose vertex is at the center of the circle

A central angle is defined as an angle whose vertex is located at the center of the circle and whose sides (or arms) extend out to intersect the circumference of the circle. This definition emphasizes the unique position of the vertex at the center, which distinguishes a central angle from other types of angles related to circles. The measure of a central angle is important in circular geometry as it correlates directly with the arc it subtends on the circle. For example, if a central angle measures 60 degrees, the arc connecting the two points where the angle's sides intersect the circle also measures 60 degrees. This property is fundamental in various mathematical applications, including calculating the area of sectors and understanding properties of inscribed angles. In contrast to other angles connected to circles, such as those formed by tangents or at points along the circumference, the central angle specifically highlights the relationship between the center of the circle and the points on its boundary, making it a key element in circle geometry concepts.