Question

Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also, measure the lengths of the tangents.

Answer 1

Radius = 5 cm, Distance = 10 cm

Steps of construction:

1. With O as centre, draw a circle of radius 5 cm.

2. Draw a line OP = 10 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 circle at A and B.

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

Verification: In the right ∆OAP

PA² = OP² – OA²

= 10² – 5²

= `sqrt(100 - 25)`

= `sqrt(75)`

= 8.7 cm

Length of the tangent is = 8.7 cm