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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.
Solution
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
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