Angle subtended by an arc

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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:

  1. With 'A' as the centre, draw a circle of any radius.
  2. Mark two points B and B' on this circle. Then, BB' is an arc of the circle.
  3. Mark point 'C' on any point on circle's circumference.
  4. Identify the angle subtended by BB' at the centre of the circle
  5. Measure the angle ∠BAB'.
  6. Identify the angle subtended by BB' at any point on the remaining part of the circle at 'C'.
  7. Measure the angle ∠BCB'.
  8. 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

  1. What do you observe if you take chord as a diameter?
  2. 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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