Question

Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 5 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.

Answer 1

Steps of Construction:

1. Draw a circle with centre O and radius 3.5 cm using a compass.
2. Mark a point P on a horizontal line such that OP = 5 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 the tangent.
Length of tangent = `sqrt(OP^2 − "radius"^2)`

= `sqrt(5^2 − 3.5^2)`

= `sqrt(25 − 12.25)`

= `sqrt(12.75)`

= 3.57 cm (approximately)

So, the length of one tangent is 3.57 cm.