Question

Draw the two tangents from a point which is 5 cm away from the centre of a circle of diameter 6 cm. Also, measure the lengths of the tangents.

Answer 1

Radius = 3cm, Distance = 5cm.

Steps of construction:

1. With O as centre, draw a circle of radius 3 cm.

2. Draw a line OP = 5 cm.

3. Draw a perpendicular bisector of OP, which cuts OP at M.

4. With M as centre and MO as radius draw a circle which cuts previous circles at A and B.

5. Join AP and BP, AP and BP are the required tangents.

The length of the tangent PA = PB = 4 cm

Verification: In the right angle triangle OAP

PA² = OP² – OA²

= 5² – 3²

= 25 – 9

= 16

PA = `sqrt(16)`

= 4 cm

Length of the tangent = 4 cm