Honors Geometry - Arcs and Central 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 intersect the circle.

Front

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

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 measures less than 180 degrees.

Front

Define a major arc.

Back

A major arc is an arc that measures more than 180 degrees.

Front

What is a semicircle?

Back

A semicircle is an arc that measures exactly 180 degrees.

Front

How do you calculate the measure of an arc?

Back

The measure of an arc can be calculated using the measure of the central angle that intercepts it.

Front

What is the formula for the circumference of a circle?

Back

The circumference C of a circle is given by the formula C = 2πr, where r is the radius.

Front

If the radius of a circle is 10, what is the circumference?

Back

The circumference is 20π or approximately 62.83.

Front

What is the formula for the length of an arc?

Back

The length L of an arc is given by L = (θ/360) * C, where θ is the central angle in degrees and C is the circumference.

Front

If a central angle is 60 degrees, what is the length of the arc in a circle with a radius of 5?

Back

The length of the arc is (60/360) * 2π(5) = (1/6) * 10π = (5/3)π or approximately 5.24.