Central angles and arcs flashcardziz

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 intersect the circle.

Front

What is the relationship between a central angle and the arc it intercepts?

Back

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

Front

Define a minor arc.

Back

A minor arc is an arc that is smaller than a semicircle, measuring less than 180 degrees.

Front

Define a major arc.

Back

A major arc is an arc that is larger than a semicircle, measuring more than 180 degrees.

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.

Front

How do you calculate the measure of an inscribed angle?

Back

The measure of an inscribed angle is half the measure of the intercepted arc.

Front

What is the formula for finding the length of an arc?

Back

Arc length = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

Front

What is the formula for finding the area of a sector?

Back

Area of a sector = (θ/360) * πr², where θ is the central angle in degrees and r is the radius.

Front

If the measure of arc JH is 130°, what is the measure of the central angle that intercepts it?

Back

The measure of the central angle is also 130°.

Front

If ∠PTQ measures 140°, what is the measure of the arc it intercepts?

Back

The measure of the arc intercepted by ∠PTQ is also 140°.