Question

Using ruler and compasses only,

1. Construct triangle ABC, having given BC = 7 cm, AB – AC = 1 cm and ∠ABC = 45°.
2. Inscribe a circle in the ΔABC constructed in (i) above. Measure its radius.

Answer 1

 
Steps of construction:

i. Construction of triangle:

a. Draw a line segment BC = 7 cm.

b. At B, draw a ray BX making an angle of 45° and cut off BE = AB − AC = 1 cm.

c. Join EC and draw the perpendicular bisector of EC intersecting BX at A.

d. Join AC.

ΔABC is the required triangle.

ii. Construction of incircle:

e. Draw angle bisectors of ∠ABC and ∠ACB intersecting each other at O.

f. From O, draw perpendiculars OL to BC.

g. O as centre and OL as radius draw circle which touches the sides of the ΔABC.

This is the required in-circle of ΔABC.

On measuring, radius OL = 1.8 cm.