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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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