(i) Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm.

(ii) Find its incenter and mark it I.

(iii) With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle.

Steps of construction :

1. Draw a line segment BC = 6 cm.

2. With B as center and radius 8 cm draw an arc.

3. With C as center and radius 5 cm draw another arc which intersects first arc at A.

4. Join AB and AC. ABC is the required triangle.

5. Draw angle bisectors of B and A intersecting each other at I. I is the incenter.

6. Through I, draw ID ⊥ AB.

7. From D as center cut off DP = DQ = $\dfrac{2}{2}$ = 1 cm.

8. With I as center and radius IP or IQ, draw a circle cutting off 2 cm chords from each side of triangle.