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Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct: 

(i) A circle of radius 2.5 cm, passing through A and C. 

(ii) Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.

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Steps of Construction:

(i) (1) Draw line AB = 5 cm 

(2) From AB cut AC = 3 cm. 

(3) Draw right bisector of AC. 

(4) Taking A as centre and AO = 2.5 cm cm as radius, draw an arc to meet the right bisector of AC at O. 

(5) Taking O as the centre and AO = 2.5 cm as radius, draw a circle, which passing through A&C. 

(6) Join BO. 

(7) Draw right bisector of BO, which cuts BO at P. 

(8) Taking P as centre and OP as radius, draw a circle which cuts old circle at R & T. 

(9) Join BR and BT. These are required tangents. 

(ii) Length of tangent = 3 cm.

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