Circle Chords, Arcs, Central Angles, Inscribed Angles

What is the relationship between the measures of arcs and their corresponding chords?

• Longer arcs correspond to longer chords.

• Shorter arcs correspond to longer chords.

• Arcs and chords have no relationship.

• All arcs correspond to equal chords.

Define an arc in the context of a circle.

• A straight line connecting two points on a circle.

• A portion of the circumference of a circle.

• The area enclosed by a circle.

• A point on the circumference of a circle.

What is the relationship between a central angle and an inscribed angle that subtends the same arc?

• The inscribed angle is equal to the central angle.

• The inscribed angle is twice the measure of the central angle.

• The inscribed angle is half the measure of the central angle.

• The inscribed angle is unrelated to the central angle.

What is a chord in a circle?

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

• A line segment with both endpoints on the circle.

• A line that touches the circle at exactly one point.

• A line segment that is longer than the radius of the circle.

What is a central angle?

• An angle whose vertex is at the center of the circle and whose sides are radii that intersect the circle.

• An angle formed by two tangents to a circle.

• An angle that is greater than 180 degrees.

• An angle formed by two chords in a circle.

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

• Area of sector = (θ/360) * πr²

• Area of sector = 2πr

• Area of sector = πr²

• Area of sector = (θ/180) * πr²

What is an inscribed angle?

• An angle formed by two chords in a circle which have a common endpoint.

• An angle formed by two tangents to a circle.

• An angle formed by a radius and a tangent to a circle.

• An angle formed by the intersection of two secants outside the circle.

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

• The measure of each angle is equal to half the sum of the measures of the arcs intercepted by the angle.

• The measure of each angle is equal to the difference of the measures of the arcs intercepted by the angle.

• The measure of each angle is equal to the sum of the measures of the arcs intercepted by the angle.

• The measure of each angle is equal to the average of the measures of the arcs intercepted by the angle.

How do you calculate the measure of an arc?

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

• The measure of an arc is equal to half the length of the arc.

• The measure of an arc is equal to the circumference of the circle divided by the radius.

• The measure of an arc is equal to the sum of the angles in the triangle formed by the endpoints of the arc.

If the measure of a central angle is 60°, what is the measure of the inscribed angle subtending the same arc?

• 20°

• 30°

• 40°

• 50°