Question

1. Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm.
2. Find its in centre and mark it I.
3. With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle. What is the length of the radius of this circle. 

Answer 1

 
Steps of construction:

1. Draw a line segment BC = 6 cm.
2. With centre B and radius 8 cm draw an arc.
3. With centre C and radius 5 cm draw another arc which intersects the first arc at A.
4. Join AB and AC.
   ΔABC is the required triangle.
5. Draw the angle bisectors of ∠B and ∠A intersecting each other at I. Then I is the incentre of the triangle ABC.
6. Through I, draw ID ⊥ AB.
7. Now from D, cut off `DP = DQ = 2/2 = 1 cm`.
8. 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.