Page 62 - Mathematics Class - IX

4. On tracing paper trace ∠AOB and fold the paper such that OA and OB coincide as shown in
Fig. (d).
C

O
O

A B
A B

Fig. (c) Fig. (d)

5. The folded trace paper will be half of the ∠AOB.
6. Place the fold at angle ∠ACB such that point O falls on C and OA along CA.
7. Repeat the activity with circles of different radii and record your observations.

OBSERVATIONS

S. No. Radius of the circle Measure of ∠AOB Measure of ∠ACB

1.

2.

3.

4.

5.

INFERENCE
This shows that the angle subtended by the arc at the centre of the circle is double the angle subtended by it at any
other point on the circumference of the circle.

EXTENDED TASK
1. Verify that all the angles in the same segment of a circle are equal by activity method.
2. Using the above theorem prove that all the angles in the same segment of a circle are equal.

APPLICATION
This property is used to prove that angles in the same segment of a circle are equal, opposite angles of a cyclic
quadrilateral are supplementary, etc.

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