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Question
Construct the incircle of the equilateral triangle whose one side is 8 cm.
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Solution
An equilateral triangle ABC in which AB=BC=CA=8 cm.
Required - To construct the given triangle ABC and to draw incircle of it.
Construction of △ABC
(1) Draw a line segment BC=8 cm.
(2) Draw an arc of radius 8 cm taking B as centre.
(3) Draw another arc of radius 8 cm. taking C as centre which intersects the previous arc at a point A.
(4) Join AB and AC.
Thus the require △ABC is constructed.
Construction of incircle of △ABC.
(1) Draw BP and CQ, the bisectors of angles ∠B and ∠C respectively to intersect each other at point O.
(2) Draw OR⊥BC which intersects BC at L.
(3) Taking O as centre and OL as radius, draw a circle which touches the sides AB, BC and CA at points N, L and M respectively.
(4) Measure the radius OL which is 2.3 cm.
Thus the required incircle is constructed and its radius is 2.3 cm.
Required - To construct the given triangle ABC and to draw incircle of it.
Construction of △ABC
(1) Draw a line segment BC=8 cm.
(2) Draw an arc of radius 8 cm taking B as centre.
(3) Draw another arc of radius 8 cm. taking C as centre which intersects the previous arc at a point A.
(4) Join AB and AC.
Thus the require △ABC is constructed.
Construction of incircle of △ABC.
(1) Draw BP and CQ, the bisectors of angles ∠B and ∠C respectively to intersect each other at point O.
(2) Draw OR⊥BC which intersects BC at L.
(3) Taking O as centre and OL as radius, draw a circle which touches the sides AB, BC and CA at points N, L and M respectively.
(4) Measure the radius OL which is 2.3 cm.
Thus the required incircle is constructed and its radius is 2.3 cm.
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