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Draw a circle of radius 5 cm. From a point 8 cm away from its centre, construct a pair of tangents to the circle. Find the lengths of tangents.

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Steps of construction : 

1) Construct a circle with a radius of 5 cm. 

2) Trace the point ‘p’ in the exterior of the circle which is at a distance of ‘8’ cm from its centre. 

3) Construct a perpendicular bisector to OP which meets at M. 

4) The draw a circle with a radius of MP or MO from the point M. This circle cuts the previous circle drawn from the centre ‘O’ at the points A and B. 

5) Now join the points PA and then PB. 

6) PA, PB are the required tangents which are measured 6.2 cm long.

OA = 5 cm ; OP = 8 cm 

AP = PB = 6.2 cm.

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