Using ruler and compasses only, draw an equilateral triangle of height 6 cm and draw its inscribed circle. Measure the radius of the circle.

Steps of construction :

1. Draw a line XY.

2. Construct perpendicular bisector of XY, let bisector intersect XY at point M.

3. From point M, draw an arc with radius 6 cm, mark the point of intersection of arc and perpendicular bisector as A.

4. Construct ∠MAB = 30° and ∠MAC = 30°.

5. Draw angle bisectors of ∠B and ∠C intersecting each other at O.

6. Draw OM perpendicular to BC. With O as center and OM as radius draw a circle, touching sides of △ABC. Measure OM.

On measuring,

OM = 2 cm.

Hence, radius of the circle = 2 cm.