Arcs, Inscribed and Central Angles

Front

What is the measure of arc AB if it corresponds to a central angle of 68 degrees?

Back

68 degrees

Front

Define 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.

Front

Define 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 two inscribed angles intercept the same arc, what can be said about their measures?

Back

They are congruent.

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 the measure of arc AB is 34 degrees, what is the measure of the inscribed angle that intercepts the same arc?

Back

17 degrees (half of the arc measure).

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

Find m∠PRQ if it intercepts an arc measuring 102 degrees.

Back

51 degrees.

Front

What is the measure of an angle formed by two tangents that intersect outside a circle?

Back

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

Front

If angle ACB is a central angle, what can be inferred about its vertex?

Back

The vertex ACB is located at the center of the circle.