Mathematics
Using ruler and compasses only,
(i) Construct triangle ABC, having given BC = 7 cm, AB - AC = 1 cm and ∠ABC = 45°.
(ii) Inscribe a circle in the △ABC constructed in (i) above.
Constructions
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Answer
(i) Steps of construction :
Draw a line segment BC = 7 cm.
At B, draw a ray BX making an angle of 45° and cut off BE = AB - AC = 1 cm.
Join EC and draw the perpendicular bisector of EC intersecting BX at A.
Join AC.
Hence, ABC is the required triangle.
(ii) Steps of construction :
Draw angle bisectors of ∠ABC and ∠ACB intersecting each other at O.
From O, draw perpendicular OL to BC.
With O as center and OL as radius draw a circle, touching sides of △ABC. Measure OL.
On measuring,
OL = 1.8 cm.
Hence, above is the required incircle of △ABC with radius = 1.8 cm.
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Using ruler and compasses only,
(i) Construct a triangle ABC with the following data :
Base AB = 6 cm, BC = 7.5 cm and angle CAB = 60°.
(ii) In same diagram, draw a circle which passes through the points A, B and C and mark its center O.
(iii) Draw a perpendicular from O to AB which meets AB in D.
(iv) Prove that : AD = BD.