Using ruler and compasses only :

(i) Construct a triangle ABC with the following data :

Base AB = 6 cm, AC = 5.2 cm and ∠CAB = 60°.

(ii) In the same diagram, draw a circle which passes through the points A, B and C, and mark its centre O.

(i) Steps of construction :

1. Draw a line segment AB = 6 cm.

2. Cut an arc of 5.2 cm from A.

3. Draw a line segment from B such that angle between the line and AB = 60°.

4. Mark the point as C where the arc from A and line segment from B meets.

5. Join points A, B and C. Hence, the △ABC is formed.

(ii) Steps of construction :

1. In the above triangle, draw the perpendicular bisector of AB and BC. Let these bisectors meet at the point O.

2. With O as center and radius equal to OA, draw a circle. The circle so drawn passes through the points A, B and C, and is required circumcircle of △ABC.