Tangent-Secant Theorem and Angles

This video tutorial explains the tangent point secant theorem, which states that the measure of an angle formed by a tangent and a secant at the point of contact is half the measure of its intercepted arc. The video provides examples to illustrate the theorem, including solving for angles ABC and TAN using given arc measures. The tutorial concludes with a final example, reinforcing the application of the theorem in geometry problem-solving.

What is the main topic discussed in this video?

• Angles formed by parallel lines

• Angles formed by secant and tangent lines

• Angles formed by intersecting lines

• Angles formed by perpendicular lines

According to the Tangent-Secant Theorem, the angle formed by a tangent and a secant is:

• Half the intercepted arc

• Twice the intercepted arc

• One-third the intercepted arc

• Equal to the intercepted arc

What is the formula used to calculate the angle formed by a tangent and a secant?

• Angle = Intercepted Arc

• Angle = 2 * Intercepted Arc

• Angle = 1/3 * Intercepted Arc

• Angle = 1/2 * Intercepted Arc

In the first example, what is the measure of arc AB?

• 360 degrees

• 180 degrees

• 270 degrees

• 90 degrees

What is the calculated measure of angle ABC in the first example?

• 270 degrees

• 180 degrees

• 90 degrees

• 135 degrees

In the first example, what is the relationship between angle ABC and arc AB?

• Angle ABC is equal to arc AB

• Angle ABC is twice arc AB

• Angle ABC is half of arc AB

• Angle ABC is one-third of arc AB

What is the measure of angle ABC in the first example if arc AB is 270 degrees?

• 180 degrees

• 135 degrees

• 270 degrees

• 90 degrees

In the second example, what is the measure of arc AT?

• 200 degrees

• 150 degrees

• 100 degrees

• 50 degrees

What is the calculated measure of angle TAN in the second example?

• 100 degrees

• 50 degrees

• 75 degrees

• 25 degrees

In the second example, what is the relationship between angle TAN and arc AT?

• Angle TAN is half of arc AT

• Angle TAN is one-third of arc AT

• Angle TAN is twice arc AT

• Angle TAN is equal to arc AT