Question

Draw a tangent to the circle from the point P having radius 3.6 cm, and centre at O. Point P is at a distance 7.2 cm from the centre.

Answer 1

Radius = 3.6, Distance = 7.2 cm.


Steps of construction:

1. With O as centre, draw a circle of radius 3.6 cm.

2. Draw a line OP = 7.2 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.

Length of the tangents PA = PB = 6.26 cm

Verification: In the right triangle ∆OAP

PA² = OP² – OA²

= 7.2² – 3.6²

= (7.2 + 3.6) (7.2 – 3.6)

PA² = 10.8 × 3.6

= ${\displaystyle \sqrt{38.38}}$

PA = 6.2 cm

Length of the tangent = 6.2 cm