Question

Using ruler and compasses only, construct  Δ ABC in which BC=7.5 cm, ∠ ABC = 60°  and AC - AB= 1.5 cm. Inscribe a circle in the Δ ABC and measure its radius. 

Answer 1

Steps of construction: 

(i) Draw a line segment BC= 7.5 cm 

(ii) At B 1 draw an arc making an angle of 60° with BC. 

(iii) At C, draw an arc with radius ( AC= AB+ 1.5 cm) = 9 cm cutting the previous arc. 

(iv) Join AC and AB. 

(v) Draw angle bisectors for ∠ A and ∠ B meeting at O. 

(vi) Draw a perpendicular to BC from O and mark it as M. 

(vii) With OM as radius draw a circle touching all three sides of the triangle. 

(viii) The drawn drde is the required circle with radius= 2.3 cm