Using ruler and compasses only construct a ΔABC in which BC = 6.2 cm, ∠A = 60° and the altitude through A is 2.6 cm. Draw the incircle of the triangle.

Steps of construction :

1. Draw a line segment BC = 6.2 cm.

2. Construct perpendicular bisector of BC, intersecting BC at point M.

3. At point B and C, construct an angle of 30°, ∠XBC = 30° and ∠YCB = 30°.

4. Let this rays XB and CY intersect at O. With center as O and radius as OB, draw major arc.

5. From M, draw an arc of radius 2.6 cm on perpendicular bisector of BC mark it as E.

6. Draw a line parallel to BC passing through E, which intersect major arc at A.

7. Join AB and AC. Hence, ABC is the required triangle.

8. Construct the angle bisector BH and CI of ∠ABC and ∠ACB respectively.

9. Let the two angle bisectors intersect at point P.

10. Draw PD perpendicular to BC. With P as centre and PD as radius, draw a circle.