Equal chords of a circle subtend equal angles at the centre Objective:

  

Topic: Equal chords of a circle subtend equal angles at the centre 

Objective:

To prove that equal chords of a circle subtend equal angles at the centre of the circle.

Pre-requisite knowledge: Construction of equal chords of a circle.

Materials required : 

(i) Drawing sheets/poster papers and tracing papers

(ii) Geometry box

(iii) Pair of scissors

(iv) Paint box

(V) Fevistick/gum.

To perform the activity :

Steps:

1. Draw a circle of any radius with centre O on a poster paper.

2. Draw two equal chords AB and CD of the circle (you may use compasses) as shown in fig. 8.1.

3. Join OA, OB, OC and OD.

4. Paint AOAB green and AOCD red as shown in fig. 8.1.

 5. Make a replica (exact copy) of AOAB from a tracing paper and paint it

blue as shown in fig. 8.2.

6. Superimpose the replica of Angle OAB on AngleOCD as shown in fig. 8.3.

Result:

We observe that the replica of triangle OAB exactly covers the triangle OCD

and note that OA falls on OC and OB falls on OD. It follows that:

Angle AOB = Angle COD

Hence equal chords of a circle subtend equal angles at the centre of the circle.