Education Technology

Secants, Tangents and Arcs

Subject Area
Math: Geometry: Circles
Level
9-12
Activity Time
45 Minutes
TI Calculator
TI-Nspire™ CX series
TI-Nspire™ CX CAS/CX II CAS
TI-Nspire Version
3.0
Resource Types
Lessons
Format
TNS

Secants, Tangents and Arcs

Activity Overview

Explore the angle and arc relationships for two intersecting lines that intersect a circle.

Objectives

  • Students will understand that if the intersection point P of two lines lies inside a circle, then the measure of the angle formed by the two secants is equal to the average of the measures of the arcs intercepted by that angle and its corresponding vertical angle.
  • Students will understand that if the intersection point P of two lines lies outside a circle, then the measure of the angle formed is equal to half of the difference of the measures of the arcs intercepted by that angle and its corresponding vertical angle, whether the lines are both secants, a secant and a tangent, or two tangents.

Vocabulary

  • Secant line and chord
  • Tangent line
  • Central angle
  • Intercepted arc

About the Lesson

This lesson involves discovering the relationship between the measure of the angle of intersection of two lines and the measures of the intercepted arcs for several cases in which two intersecting lines intersect a circle.

  • If the intersection point P of two lines lies inside a circle, then the measure of the angle formed by the two secants is equal to the average of the measures of the arcs intercepted by that angle and its corresponding vertical angle.
  • If the intersection point P of two lines lies outside a circle, then the measure of the angle formed is equal to half of the difference of the measures of the arcs intercepted by that angle and its corresponding vertical angle, whether the lines are both secants, a secant and a tangent, or two tangents.

Subject Area
Math: Geometry: Circles
Level
9-12
Activity Time
45 Minutes
TI Calculator
TI-Nspire™ CX series
TI-Nspire™ CX CAS/CX II CAS
TI-Nspire Version
3.0
Resource Types
Lessons
Format
TNS
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