Question

Draw a triangle whose sides are 6 cm, 5 cm and 6 cm and inscribe a circle in it. Find by measurement its radius.

Answer 1

Given:

A ΔABC in which AB = 6 cm, BC = 5 cm, and CA = 6 cm.

Required: To construct the incircle of ΔABC.

Steps of Construction:

1. Draw a line segment AB = 6 cm.
2. With A as the centre and radius 6 cm, draw an arc.
3. With B as centre and radius 5 cm, draw another arc intersecting the first arc at C.
4. Join A to C and B to C.
   Then ΔABC is the required triangle.
5. Draw the bisectors of angles ∠CAB and ∠ABC.
   These angle bisectors intersect at point I.
   Then I is the incentre of ΔABC.
6. Draw ID ⟂ AB.
   (From I, draw a perpendicular to the base AB. Let the foot of the perpendicular be D.)
7. Draw a circle with I as the centre and radius equal to ID.
   This is the required incircle of ΔABC.
8. By measurement, radius ID ≈ 1.4 cm.