Question

Draw a circle of radius 6 cm. Mark a point at a distance of 9 cm from the centre. Construct two tangents to the circle from this point. Measure the length of each tangent.

Answer 1

 

Steps of Construction:

1. Draw a circle with centre O and radius 6 cm using a compass.
2. Mark a point P on a horizontal line such that OP = 9 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.
   This circle will cut the given circle at two distinct points, A and B.
6. Join PA and PB.
7. PA and PB are the required tangents from point P to the given circle.

Measure the length of each tangent.

Length of tangent = `sqrt(OP^2 − "radius"^2)`

= `sqrt(9^2 − 6^2)`

= `sqrt(81 − 36)`

= `sqrt45`

= 6.70 cm (approximately)

So, the length of each tangent is 6.70 cm.