Honors Geometry - Arcs and Central Angles

Front

What is the measure of a central angle in a circle?

Back

A central angle is the angle whose vertex is at the center of the circle and whose sides are radii that intersect the circle. Its measure is equal to the measure of the arc it intercepts.

Front

Define a minor arc.

Back

A minor arc is an arc of a circle that is smaller than a semicircle, measuring 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

If the measure of arc AB is 120°, what is the measure of the central angle AOB?

Back

The measure of the central angle AOB is equal to the measure of arc AB, which is 120°.

Front

What is the relationship between the measures of an inscribed angle and the arc it intercepts?

Back

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

Front

Calculate the measure of arc AC if arc ABC measures 210° and arc AB measures 60°.

Back

The measure of arc AC is 210° - 60° = 150°.

Front

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

Back

The length of an arc can be found using the formula: Length = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

Front

If the radius of a circle is 10 cm and the central angle is 90°, what is the length of the arc?

Back

Length = (90/360) * 2π(10) = (1/4) * 20π = 5π cm.

Front

What is the measure of a semicircle?

Back

A semicircle measures exactly 180 degrees.

Front

If two arcs of a circle are congruent, what can be said about their corresponding central angles?

Back

If two arcs are congruent, their corresponding central angles are also congruent.