Mathematics
Using ruler and compasses only, draw an equilateral triangle of side 5 cm and draw its inscribed circle. Measure the radius of the circle.
Constructions
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Answer
Steps of construction :
Draw a line segment BC = 5 cm.
From B and C cut an arc of 5 cm.
Mark the point as A which is intersection of the two arcs.
Join A, B and C. Hence, the equilateral △ABC is formed.
Draw the (internal) bisectors of ∠B and ∠C. Let these bisectors meet at point I.
From I, draw IN perpendicular to the side BC.
With I as centre and radius equal to IN, draw a circle. The circle so drawn touches all the sides of the △ABC, and is the required incircle of △ABC.
On measuring IN, we get the radius of the incircle.
Hence, the radius of the incircle = 2.3 cm.
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