Question

Take a point which is 11 cm away from the centre of a circle of radius 4 cm and draw the two tangents to the circle from that point.

Answer 1

Radius = 4 cm, Distance = 11 cm


Steps of construction:

1. With O as centre, draw a circle of radius 4 cm.

2. Draw a line OP = 11 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 the previous circles A and B.

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

This the length of the tangents PA = PB = 10.2 cm

Verification: In the right angle triangle OAP

PA² = OP² – OA²

= 11² – 4²

= 121 – 16

= 105

PA = `sqrt(105)`

= 10.2 cm

Length of the tangents = 10.2 cm