Education Technology

Angles Formed by Intersecting Chords, Secants, and Tangents

Published on 06/09/2008

Activity Overview

In this activity, students will investigate properties of angles and arcs formed when chords, secants, and tangents intersect and intercept arcs in a circle. They discover several important theorems concerning circles and arc sizes. They make use of the Central Angle theorem, which ensures that the measure of a central angle of a circle is equal to the measure of its intercepted arc.

Before the Activity

  • Install the Cabri Jr. App on the students' graphing calculators using TI Connect™, a TI Connectivity Cable and the Unit-to-Unit Link Cable
  • Use the TI-Navigator™ to transfer the attached Cabri Jr. AppVar files to each calculator
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 179 - 183 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to your class.

    Follow the Activity procedures:

  • Use the AppVar to go directly to the exploration section
  • Construct an angle inscribed in a circle and its corresponding central angle
  • Drag the points and observe changes in the angles
  • Construct a circle with two intersecting chords
  • Construct a circle with two secants that intersects outside the circle
  • Construct a circle which has a tangent and a chord that intersect at a point
  • Use the Calculate tool to investigate the relationship between the angles formed by the chords
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary