Draw two tangents from a point 7 cm away from the centre of a circle of radius 4 cm

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Radius = 4 cm, Distance = 11 cm

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

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