Central and Inscribed Angles

Front

What is a central angle?

Back

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

Front

How do you find the measure of a central angle?

Back

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

Front

How do you find the measure of an inscribed angle?

Back

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

Front

What is the relationship between a central angle and an inscribed angle that intercept the same arc?

Back

The central angle is twice the measure of the inscribed angle.

Front

If the measure of arc AB is 80°, what is the measure of the inscribed angle that intercepts arc AB?

Back

40° (because the inscribed angle is half of the arc measure).

Front

What is the measure of a semicircle?

Back

180°.

Front

If a diameter of a circle is one side of an inscribed angle, what is the measure of that angle?

Back

90° (because the inscribed angle subtended by a diameter is always a right angle).

Front

What is the formula for the measure of an arc?

Back

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

Front

If the measure of arc XY is 54°, what is the measure of the central angle that intercepts arc XY?

Back

54° (the central angle is equal to the arc measure).