Circle Theorems and Angle Relationships

The video tutorial covers various theorems related to circles, including the tangent and intersected chord theorem, intersecting lines and circle theorems, and the circumscribed angle theorem. It provides examples and diagrams to illustrate these concepts and concludes with a word problem involving the northern lights, demonstrating the application of these theorems in real-world scenarios.

What does the tangent and intersected chord theorem state about the measure of angles formed?

• Each angle is twice the measure of its intercepted arc.

• Each angle is half the measure of its intercepted arc.

• Each angle is equal to the measure of its intercepted arc.

• Each angle is three times the measure of its intercepted arc.

In the tangent and intersected chord theorem, if the intercepted arc measures 130°, what is the measure of the angle?

• 65°

• 130°

• 260°

• 90°

When two lines intersect inside a circle, what is the relationship between the angle and its intercepted arcs?

• The angle is the difference of the intercepted arcs.

• The angle is half the sum of the intercepted arcs.

• The angle is equal to the sum of the intercepted arcs.

• The angle is twice the sum of the intercepted arcs.

How do you calculate the measure of an angle formed outside a circle by two tangents?

• Add the intercepted arcs and multiply by two.

• Multiply the intercepted arcs by two.

• Subtract the intercepted arcs and divide by two.

• Add the intercepted arcs and divide by two.

What does the circumscribed angle theorem state about the measure of a circumscribed angle?

• It is half the central angle.

• It is twice the central angle.

• It is 180° minus the central angle.

• It is equal to the central angle.

In the northern lights problem, what is the measure of the central angle if the intercepted arc is 25.4°?

• 180°

• 12.7°

• 25.4°

• 50.8°