Arc & Angles of Circles

Front

What is the definition of a circle?

Back

A circle is a set of points in a plane that are equidistant from a fixed point called the center.

Front

What is the measure of a full circle in degrees?

Back

360 degrees.

Front

What is an arc in a circle?

Back

An arc is a portion of the circumference of a circle.

Front

What is the relationship between the central angle and the arc it subtends?

Back

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

Front

What is the formula for finding the measure of an inscribed angle?

Back

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

Front

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

Back

The measures of the two angles are equal.

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 half the difference of the measures of the intercepted arcs.

Front

What is the formula for 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

What is the formula for the area of a sector of a circle?

Back

Area of sector = (θ/360) × πr², where θ is the central angle in degrees and r is the radius.

Front

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

Back

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