Exploring Central Angles and Inscribed Angles

This video tutorial covers the basics of circles in geometry, focusing on central and inscribed angles, chords, diameters, and arc measures. It explains the properties of circles, including the relationships between different types of angles and arcs. The inscribed angle theorem is introduced and proven, providing a comprehensive understanding of how angles and arcs interact within a circle.

What is a central angle in a circle?

• An angle with its vertex outside the circle

• An angle with its vertex at the center of the circle

• An angle formed by two intersecting chords

• An angle with its vertex on the circle

What defines a semicircle?

• An arc that is exactly 180 degrees

• An arc that is more than 180 degrees

• An arc that is less than 180 degrees

• An arc that covers the entire circle

How is the measure of a minor arc determined?

• It is one-fourth the measure of its central angle

• It is equal to the measure of its central angle

• It is twice the measure of its central angle

• It is half the measure of its central angle

What is true about the measure of a major arc?

• It is equal to the measure of its central angle

• It is equal to 360 minus the measure of its central angle

• It is half the measure of its central angle

• It is twice the measure of its central angle

What is the measure of an arc if its central angle is 90 degrees?

• 45 degrees

• 90 degrees

• 180 degrees

• 360 degrees

What is the relationship between an inscribed angle and its intercepted arc?

• The inscribed angle is half the measure of its intercepted arc

• The inscribed angle is equal to the measure of its intercepted arc

• The inscribed angle is twice the measure of its intercepted arc

• The inscribed angle is one-fourth the measure of its intercepted arc

If an inscribed angle intercepts a diameter, what type of angle is it?

• Acute angle

• Obtuse angle

• Straight angle

• Right angle

How can the measure of an arc be calculated if it is intercepted by an inscribed angle of 40 degrees?

• 20 degrees

• 160 degrees

• 40 degrees

• 80 degrees

In a circle, adjacent arcs share which of the following?

• A common central angle

• A common radius

• A common endpoint

• A common diameter

What theorem is used to determine that an inscribed angle is a right angle when it intercepts a diameter?

• Inscribed Angle of a Diameter Theorem

• Inscribed Angle Theorem

• Central Angle Theorem

• Arc Addition Postulate