Exploring Central and Inscribed Angles

This video tutorial delves into the characteristics of central and inscribed angles in circles. It begins with a recap of central angles, explaining that they have their vertex at the circle's center and their arc measure equals the angle's measure. The video then explores inscribed angles, which have their vertex on the circle, and introduces the inscribed angle theorem, stating that an inscribed angle's measure is half that of its intercepted arc. The tutorial concludes with a preview of the next lesson on inscribed polygons and puzzles.

What defines a central angle in a circle?

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

• An angle that intersects the circle at one point

• An angle with its vertex on the circle

• An angle with its vertex outside the circle

What is created when a central angle intersects a circle?

• Only a major arc

• A minor and a major arc

• A tangent line

• Only a minor arc

What is the measure of an arc intercepted by a central angle?

• One-third the measure of the central angle

• Half the measure of the central angle

• The same as the measure of the central angle

• Twice the measure of the central angle

What can be said about the arcs created by central angles?

• They are always minor arcs

• They can be either minor or major arcs

• They are always major arcs

• They cannot be defined

How is the vertex of an inscribed angle positioned?

• Outside the circle

• At the center of the circle

• On the circle

• Inside the circle

How are the radii related to an inscribed angle's intercepted arc?

• They are perpendicular to the arc

• They divide the circle into equal parts

• They bisect the arc

• They are congruent to each other

What is true about the angles in an isosceles triangle formed by radii in a circle?

• All three angles are congruent

• They are all acute angles

• They are all obtuse angles

• Two angles are congruent

What does the Inscribed Angle Theorem state?

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

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

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

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

How does the measure of an inscribed angle compare to its central angle?

• It is triple

• It is double

• It is the same

• It is half

Which statement best describes the relationship between an inscribed angle and its intercepted arc according to the Inscribed Angle Theorem?

• The angle's measure is double the arc's measure

• The angle's measure is half of the arc's measure

• The angle's measure is unrelated to the arc's measure

• The angle's measure is equal to the arc's length