Mathematics Lab Activity-16 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 - 16
Objective
To verify that the lengths of tangents to a circle from some external point are equal.
Glazed papers of different colours, geometry box, sketch pen, scissors, cutter and glue.
1. Draw a circle of any radius, with centre O on a coloured glazed paper of a convenient size [see Fig. 1].
Figure 1
2. Take any point P outside the circle.
3. Place a ruler touching the point P and the circle, lift the paper and fold it to create a crease passing through the point P [see Fig. 2].
Figure 2
4. Created crease is a tangent to the circle from the point P. Mark the point of contact of the tangent and the circle as Q. Join PQ [see Fig. 3].
Figure 3
5. Now place ruler touching the point P and the other side of the circle, and fold the paper to create a crease again [see Fig. 4].
Figure 4
6. This crease is the second tangent to the circle from the point P. Mark the point of contact of the tangent and the circle as R. Join PR [see Fig. 5].
Figure 5
7. Join the centre of the circle O to the point P [see Fig. 6].
Figure 6
Observations & calculations1. Fold the circle along OP.
2. We observe that Q coincides with R. Therefore, QP = RP, i.e.,
length of the tangent QP = length of the tangent RP.
On actual measurement:
3. Length of tangent QP = 4 cm
4. Length of tangent RP = 4 cm
So, length of tangent QP = length of tangent RP
Result
From this we conclude that length of tangent drawn from external point to the circle are equal.
Applications
This result is useful in solving problems in geometry and mensuration.
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