Arcs, Inscribed and Central Angles

Front

What is an arc in a circle?

Back

An arc is a portion of the circumference of a circle, defined by two endpoints on the circle.

Front

Define inscribed angle.

Back

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

Front

What is a central angle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii that extend to the circle.

Front

How do you calculate the measure of an arc?

Back

The measure of an arc can be calculated using the formula: Arc Measure = Central Angle Measure.

Front

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

Back

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

Front

If the measure of arc AB is 68°, what is the measure of ∠AOB?

Back

The measure of ∠AOB is 68° because it is a central angle.

Front

If the measure of arc DC is 122°, what is the measure of ∠DIC?

Back

The measure of ∠DIC is 61° because it is an inscribed angle that intercepts arc DC.

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

How do you find the measure of an angle formed by two intersecting chords?

Back

The measure of the angle is equal to half the sum of the measures of the arcs intercepted by the angle.

Front

If arc ABC measures 210°, what is the measure of ∠AOC?

Back

The measure of ∠AOC is 105° because it is half of the arc ABC.