Page 66 - Mathematics Class - X

ACTIVITY 4.6

OBJECTIVE
To verify that the lengths of tangents to a circle from external point are equal.

MATERIALS REQUIRED
Coloured papers (any two colours) A pair of scissors and a pencil
Geometry box, sketch, pens, adhesive
C
PRE-REQUISITE KNOWLEDGE Tangent
Concept of tangent to a circle. Point of contact
G
THEORY
1. Tangent: Any line which touches the circle at any point.
D
2. Point of contact: The point at which the tangent touches the circle.

PROCEDURE
1. Draw a circle of suitable radius on a coloured paper and cut it. Let O be its centre.
2. Paste the cutout on a rectangular sheet of paper (Fig. (a)).
3. Take any point A outside the circle.

4. From A fold the paper in such a way that it just touches the circle so we get a tangent AP (P is the point of
contact) (Fig. (b)). Join AP.

5. Repeat step 4 to get another tangent AQ to the circle (Q is the point of contact) (Fig. (c)). Join AQ.

A

O

Fig. (a) Fig. (b) Fig. (c)

6. Join the centre of the circle O to A, P and Q. (Fig. (d) and (e))
7. Fold the paper along OA (Fig. (e)). What do you observe?

Fig. (d) Fig. (e)

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