Question

Using a ruler and a compass construct a triangle ABC in which AB = 7 cm, ∠CAB = 600 and AC = 5 cm. Construct the locus of : 

(i) points equidistant from AB and AC. 

(ii) points equidistant from BA and BC. Hence, construct a circle touching the three sides of the triangle internally

Answer 1

Steps of Construction :

1. Draw a line segment AB = 7 cm. 

2. At A construct an angle of 600 such that AC = 5 cm. 

3. Join BC to get ∆ABC. 

(i) Draw angle bisector of ∠BAC, which is the required locus of the points equidistant from AB and AC. 

(ii) Draw angle bisector of ∠ABC, which is the required locus of the points equidistant from BA and BC. 

4. Let the two angle bisectors intersect each other in I.

5. Through I, draw ID⊥AB. With I as centre and radius = ID draw a circle which touches all the sides of the ∆ABC internally.