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 a central angle.

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides (rays) extend to the circumference.

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. The vertex of the angle is on the circle.

Front

How do you calculate the measure of an arc?

Back

The measure of an arc is equal to the measure of the central angle that subtends the arc.

Front

If the measure of arc ABC is 210°, what is the measure of the inscribed angle ACB?

Back

The measure of the inscribed angle ACB is half the measure of the arc ABC, so it is 105°.

Front

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

Back

The measure of a central angle is equal to the measure of its intercepted arc.

Front

How do you find the measure of an inscribed angle?

Back

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

Front

What is the formula for the measure of an arc in terms of the central angle?

Back

The measure of the arc (in degrees) is equal to the measure of the central angle.

Front

If angle AOC is a central angle measuring 150°, what is the measure of arc AC?

Back

The measure of arc AC is also 150°.

Front

What is the measure of an angle formed by two tangents drawn from a point outside a circle?

Back

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