Flashcard on Arcs, Inscribed and Central Angles

Front

What is the definition of a central angle?

Back

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

Front

What is the definition of 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

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

Back

150°

Front

What is the relationship between a central angle and the arc it intercepts?

Back

The measure of a central angle is equal to the measure of the arc it intercepts.

Front

If an inscribed angle intercepts an arc of 80°, what is the measure of the inscribed angle?

Back

40° (The inscribed angle is half the measure of the intercepted arc.)

Front

What is the formula to find the measure of an inscribed angle?

Back

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

Front

Determine if the angle is a central angle, inscribed angle or neither: ∠ACB.

Back

Central angle (if A and B are points on the circle and C is the center).

Front

What is the measure of arc DC if the central angle ∠DOC = 244°?

Back

244° (The measure of the arc is equal to the measure of the central angle.)

Front

If the measure of arc AB is 98°, what is the measure of the inscribed angle that intercepts arc AB?

Back

49° (The inscribed angle is half the measure of the intercepted arc.)

Front

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

Back

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