Angle Relationships in Circles

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, and the sides of the angle are the chords.

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 intercepted arc.

Front

If the measure of arc AB is 68°, what is the measure of the inscribed angle that intercepts arc AB?

Back

34°

Front

What is the measure of 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 find the measure of an angle formed by two tangents to a circle?

Back

The measure of the angle formed by two tangents to a circle from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.

Front

What is the measure of an angle formed by a tangent and a chord?

Back

The measure of the angle formed by a tangent and a chord through the point of contact is equal to half the measure of the intercepted arc.

Front

What is the relationship between angles formed by two intersecting chords?

Back

The measure of the angle formed by two intersecting chords is equal to half the sum of the measures of the intercepted arcs.

Front

If two chords intersect inside a circle, how do you find the measure of the angles formed?

Back

The measure of each angle formed by the intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Front

What is the formula for finding the measure of an angle formed by two secants?

Back

The measure of the angle formed by two secants drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.

Front

If angle 1 measures 65°, what is the measure of the arc it intercepts?

Back

130° (since the inscribed angle is half the measure of the intercepted arc).