Mathematics Lab Activity-11 Class IX | Circle

  Lab Activity-11 Class iX

Mathematics Lab Activities on Circle for class IX students, with complete observation tables, strictly according to the CBSE syllabus.

Chapter - 09  circle

Activity - 11

Objective: 

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

Material Required

Cardboard, coloured drawing sheets, scissors, sketch pens, adhesive, geometry box, transparent sheet.

Procedure

1. Take a rectangular cardboard of a convenient size and paste a white paper on it.

2. Cut out a circle of suitable radius on a coloured drawing sheet and paste on the cardboard.

3. Take two points B and C on the circle to obtain the arc BC [see Fig. 1].

4. Join the points B and C to the centre O to obtain an angle subtended by the arc BC at the centre O.

5. Take any point A on the remaining part of the circle. Join it to B and C to get ∠BAC subtended by the arc BC on any point A on the remaining part of the circle [see Fig. 1].

Figure 1

6. Make a cut-out of ∠BOC using transparent sheet [see Fig. 2].

Figure 2

Make a cut-out of   ∠BAC, using transparent sheet [see Fig. 3].

Figure 3

7. Place the two cut-outs of ∠BAC on the cut-out of ∠BOC, adjacent to each as shown in the Fig. 4.

Figure 4

8. Clearly, 2 ∠BAC = ∠BOC, i.e., 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.

Observations

Measure of ∠BOC = 140^o.

Measure of ∠BAC = 70^o.

Therefore, ∠BOC = 2 × ∠BAC.

Result : 

With this activity we prove that angle made by an arc at the centre is double the angle by the same are in the remaining part of the circle.

Applications

This property is used in proving many other important results such as angles in the same segment of a circle are equal, opposite angles of a cyclic quadrilateralare supplementary, etc..

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