Angles in a circle subtended by a chord

From Karnataka Open Educational Resources

The angle made at the centre of a circle by the radii at the end points of a chord is called the central angle or angle subtended by a chord at the centre.


Understand different angles subtended by a chord in a circle

Estimated Time

30 minutes

Prerequisites/Instructions, prior preparations, if any

Prior knowledge of point, lines, angles, polygons

Materials/ Resources needed

  • Digital : Computer, geogebra application, projector.
  • Non digital : Worksheet and pencil, compass, strings
  • Geogebra files : Angle subtended by chord.ggb

Download this geogebra file from this link.

Process (How to do the activity)

  • Two equal chords are drawn, the endpoints are joined to the center of the circle to form triangles.
  • What can you say of the angles subtended by the two chords? How are the two subtended angles equal. Compare triangles formed.
  • When is the subtended angle the largest?
  • If the angles subtended are equal will the chords be of equal measure?

HW Activity : Draw circle, at the center draw two angles of equal measure. Mark the chords formed by the angles. Measure the lengths of the two chords. Note your observations.