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 incentre 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.
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 incentre 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 for construction:

i) Draw a line segment BC = 6 cm.

ii) Draw an arc with centre B and radius 8 cm.

iii) Draw another arc with centre C and radius 5 cm which intersects the first arc at A.

iv) Join AB and AC.

Therefore,, ΔABC is the required triangle.

v) Draw the angle bisectors of ∠B and ∠A which intersect each other at I. Then I is the incentre of the triangle ABC.

vi) Through I, draw ID ⊥ AB.

vii) Now from D, cut off DP = DQ = 2/2 = 1 cm

viii) With centre I, and radius IP or IQ, draw a circle which will intersect each side of triangle ABC cutting chords of 2 cm each.