Question

Use ruler and compass only for answering this question.

Draw a circle of radius 4 cm. Mark the centre as O. Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents to the circle from the external point P.

Measure and write down the length of any one tangent.

Answer 1

Steps of Construction:

1. Draw a circle with centre O and radius 4 cm using a compass.
2. Mark a point P on a horizontal line such that OP = 7 cm.
3. Join OP.
4. Draw the perpendicular bisector of OP to obtain its midpoint, say M.
5. With M as centre and radius MO, draw a circle.
6. This circle will cut the given circle at two distinct points A and B.
7. Join PA and PB.
8. PA and PB are the required tangents from the external point P to the given circle.

Measure the length of the tangent.

Length of tangent

`sqrt(OP^2 − "radius"^2)`

= `sqrt(7^2 − 4^2)`

= `sqrt(49 − 16)`

= `sqrt(33)`

= 5.74 cm (approximately)

So, the length of one tangent is 5.74 cm.