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Question
Construct the circumcircle and incircle of an equilateral triangle ABC with side 6 cm and centre O. Find the ratio of radii of circumcircle and incircle.
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Solution
Construction:-
Steps of Construction:-
- Construct an equilateral triangle Δ ABC with side 6 cm.
- Draw perpendicular bisectors of any two sides. Let O be the point of intersection.
- Draw a circle with centre O and radius OA or OB or OC. This gives us circumcircle equilateral triangle Δ ABC.
- Draw the bisector of ∠C . It passes through centre of the circle O.
- Draw a circle with radius OM. This gives us incircle of the equilateral triangle Δ ABC.
In an equilateral triangle angle bisector and median are same, also circumcentre and incentre are same. For equilateral triangle circumcentre divides the median in 2:1.
So the ratio of radii of circumcircle and incircle is 2:1.
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