# 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.

### Objectives

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.