Central and Inscribed Angles

Front

What is a central angle?

Back

A central angle is an angle whose vertex is at the center of a circle and whose sides are radii that extend to the circle's circumference.

Front

What is an inscribed angle?

Back

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. The vertex of the angle is on the circle.

Front

How is the measure of a central angle related to the arc it intercepts?

Back

The measure of a central angle is equal to the measure of the arc it intercepts.

Front

How is the measure of an inscribed angle related to the arc it intercepts?

Back

The measure of an inscribed angle is half the measure of the arc it intercepts.

Front

What is a minor arc?

Back

A minor arc is an arc of a circle that measures less than 180 degrees.

Front

What is a major arc?

Back

A major arc is an arc of a circle that measures greater than 180 degrees.

Front

What is the relationship between a central angle and a major arc?

Back

The central angle that intercepts a major arc is greater than 180 degrees.

Front

What is the relationship between a central angle and a minor arc?

Back

The central angle that intercepts a minor arc is less than 180 degrees.

Front

If the measure of arc AYB is 260 degrees, what is the measure of the inscribed angle that intercepts it?

Back

The measure of the inscribed angle is 130 degrees, which is half of 260 degrees.

Front

If a central angle measures 115 degrees, what is the measure of the corresponding arc?

Back

The measure of the corresponding arc is also 115 degrees.