Central Angles and Arc Measures

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

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

• The measure of the arc is twice the measure of the central angle that subtends it.

• The measure of the arc is half the measure of the central angle that subtends it.

• The measure of the arc is unrelated to the measure of the central angle that subtends it.

What is a major arc?

• An arc that measures exactly 180 degrees.

• An arc that is smaller than a semicircle, measuring less than 180 degrees.

• An arc that is larger than a semicircle, measuring more than 180 degrees.

• An arc that is equal to the circumference of a circle.

What is the significance of the chord in relation to the circle?

• A chord can be used to define segments of the circle and can also help in determining the circle's area and other properties.

• A chord is a line that connects two points on the circle's circumference without passing through the center.

• A chord is the longest distance across the circle, also known as the diameter.

• A chord divides the circle into two equal halves, creating two semicircles.

Define a diameter in the context of a circle.

• A diameter is a straight line segment that passes through the center of a circle and connects two points on the circumference, effectively dividing the circle into two equal halves.

• A diameter is the longest chord in a circle that does not pass through the center.

• A diameter is a line segment that connects any two points on the circumference of a circle.

• A diameter is a line that runs parallel to the radius of a circle.

What is a central angle?

• An angle whose vertex is at the center of a circle and whose sides are radii that extend to the circumference.

• An angle formed by two tangents to a circle from a point outside the circle.

• An angle whose vertex is on the circumference of the circle and whose sides are chords of the circle.

• An angle that measures more than 180 degrees and is located outside the circle.

What is the difference between a minor arc and a major arc?

• A minor arc is larger than a semicircle, measuring more than 180 degrees, while a major arc is smaller than a semicircle, measuring less than 180 degrees.

• A minor arc is an arc that is smaller than a semicircle, measuring less than 180 degrees, while a major arc is larger than a semicircle, measuring more than 180 degrees.

• A minor arc is an arc that measures exactly 180 degrees, while a major arc is any arc that measures less than 180 degrees.

• A minor arc is an arc that is equal to a semicircle, measuring exactly 180 degrees, while a major arc is any arc that measures more than 180 degrees.

What is the formula for the circumference of a circle?

• C = πd

• C = 2πr

• C = πr^2

• C = 2r

What is a chord in a circle?

• A line segment whose endpoints both lie on the circumference of the circle.

• A line that passes through the center of the circle.

• A point on the circumference of the circle.

• A line segment that connects the center of the circle to a point on the circumference.

How do you calculate the measure of an arc?

• (central angle/360) * circumference of the circle

• (central angle/180) * diameter of the circle

• (central angle/360) * area of the circle

• (central angle/90) * radius of the circle

What is the relationship between the diameter and the radius of a circle?

• The diameter is equal to the radius.

• The diameter is half the length of the radius.

• The diameter is twice the length of the radius; thus, D = 2r.

• The diameter is the same as the circumference.