Mathematics Lab Activity-15 Class X | Tangent to a Circle

 Mathematics Lab Activity-15 Class X

Mathematics Laboratory Activities on Tangent to a Circle for class X students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 10

tangent to a circle

Activity - 15

Objective

To verify experimentally that the tangent at any point to a circle is perpendicular to the radius through that point.

Material Required

Coloured chart paper, adhesive, scissors/cutter, geometry box, cardboard.

Procedure

1. Take a coloured chart paper of a convenient size and draw a circle of a suitable radius on it. Cut out this circle and paste it on a cardboard.

2. Take points P, Q and R on the circle [see Fig. 1].

3. Through the points P, Q and R form a number of creases and select those which touch the circle. These creases will be tangents to the circle.

Figure 1

4. Let the creases intersect at the points A, B and C forming a △ABC ( creases has been shown by dotted lines)

5. The circle now can be taken as incircle of △ABC with O as its centre. Join OP, OQ and OR.

6. Take points P1 and P2 on the crease BC.

Observations & calculations

Take triangles POP1 and POP2

Clearly OP1 > OP, OP2 > OP.

In fact, OP is less than any other line segment joining O to any point on BC other than P, i.e., OP is the shortest of all these.

Therefore, OP ⊥ BC.

Hence, tangent to the circle at a point is perpendicular to the radius through that point.

Similarly, it can be shown that OQ ⊥ AC and OR ⊥ AB.

By actual measurement:

OP = 3 cm, OQ = 3 cm, OR = 3 cm

OP1 = 3.2 cm,  OP2 = 3.6 cm

OP < OP1, OP ........... OP2

Therefore, OP ⊥ BC

Thus, the tangent is PERPENDICULAR to the radius through the point of contact.

Result

From this we conclude that in a circle radius is always perpendicular to the tangent at the point of contect.

Applications

This result can be used in proving various other results of geometry.

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