Central Angles, Arc Measure, and Arc Length

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

How is the measure of an arc determined?

Back

The measure of an arc is determined by the central angle that subtends it, measured in degrees.

Front

What is the formula for arc length?

Back

Arc Length = (θ/360) × 2πr, where θ is the central angle in degrees and r is the radius of the circle.

Front

If the radius of a circle is 10 cm and the central angle is 60 degrees, what is the arc length?

Back

Arc Length = (60/360) × 2π(10) = 10.47 cm.

Front

What is the relationship between the central angle and the arc length?

Back

The larger the central angle, the longer the arc length, assuming the radius remains constant.

Front

Define a minor arc.

Back

A minor arc is an arc that is smaller than a semicircle, subtended by a central angle less than 180 degrees.

Front

Define a major arc.

Back

A major arc is an arc that is larger than a semicircle, subtended by a central angle greater than 180 degrees.

Front

What is the measure of a semicircle?

Back

The measure of a semicircle is 180 degrees.

Front

If arc AB measures 140 degrees, what is the measure of the remaining arc (arc ACB)?

Back

The measure of arc ACB is 360 - 140 = 220 degrees.

Front

How do you convert arc length from degrees to radians?

Back

To convert degrees to radians, multiply by π/180.