Education Technology

Angles Formed by Intersecting Chords, Secants, and Tangents

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