# Class 10 Maths Activity- To verify that the lengths of tangents to a circle from some external point are equal.

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

MATERIAL REQUIRED
Glazed papers of different colours, geometry box, sketch pen, scissors, cutter and glue

METHOD OF CONSTRUCTION
1. Draw a circle of any radius, say 3 cm, with centre O on a coloured glazed paper of a convenient size.

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 P

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.

5. Now place ruler touching the point P and the other side of the circle, and fold the paper to create a crease again.

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.

7. Join the centre of the circle O to the point P.

DEMONSTRATION

1. 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.
This verifies the result.

OBSERVATION
On actual measurement:
1. Length of tangent QP = 7.5 cm
2. Length of tangent RP = 7.5 cm
So, length of tangent QP = length of tangent RP

APPLICATION
This result is useful in solving problems in geometry and mensuration.  