Using ruler and compasses only, construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and the perpendicular from A on BC is 2.5 cm. Draw the circumcircle of triangle ABC and measure its radius.

Steps of construction :

1. Draw a line segment BC = 4 cm.

2. At B, draw a perpendicular and cut off BE = 2.5 cm.

3. From E, draw a line EF parallel to BC.

4. From C, draw a ray making an angle of 45° which intersects EF at A.

5. Join AB.

6. Draw a line AD parallel to BE. This AD is the perpendicular bisector of BC.

7. Draw the perpendicular bisectors of sides BC and AC intersecting at O.

8. With centre O and radius OB or OC or OA draw a circle which will pass through A, B and C. This is the circumcircle of △ABC.

On measuring OB we get the radius of the circumcircle.

Hence, the radius of circumcircle = 2 cm.