Mathematics
Using ruler and compasses only :
(i) Construct a triangle ABC with the following data :
BC = 7 cm, AB = 5 cm and ∠ABC = 45°.
(ii) Draw the inscribed circle to △ABC drawn in part (i).
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 BA = 5 cm.
Join AC.
Hence, the required triangle ABC is formed.
(ii) Steps of construction :
Draw the angle bisectors of ∠B and ∠C intersecting each other at I.
From I draw a perpendicular ID on BC.
With centre as I and radius ID, draw a circle which touches all the sides of △ABC.
This is the required inscribed circle to △ABC.
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