# Angle subtended by an arc

From Karnataka Open Educational Resources

### Objectives

To understand the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

### Estimated Time

30 minutes

### Prerequisites/Instructions, prior preparations, if any

knowledge about circle, circumference of circle, chord of a circle, arc of a circle, angle at centre

### Materials/ Resources needed

Digital: Click here to open the file

Non-digital: paper, pencil, ruler, compass, protractor

### Process (How to do the activity)

Download this geogebra file from this link.

**Procedure:**

- With 'A' as the centre, draw a circle of any radius.
- Mark two points B and B' on this circle. Then, BB' is an arc of the circle.
- Mark point 'C' on any point on circle's circumference.
- Identify the angle subtended by BB' at the centre of the circle
- Measure the angle ∠BAB'.
- Identify the angle subtended by BB' at any point on the remaining part of the circle at 'C'.
- Measure the angle ∠BCB'.
- Verified that the angle ∠BAB' subtended by an arc at the centre of a circle is double the angle ∠BCB' subtended by it at any point on the remaining part of the circle.i.e. ∠BAB'=2∠BCB'

### Evaluation at the end of the activity

- What do you observe if you take chord as a diameter?
- If the angle at the centre is 60°, what will be the angle on the remaining part of circle subtended by an arc ?

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