SSC (Marathi Semi-English) 10thMaharashtra State Board
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# 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. - SSC (Marathi Semi-English) 10th - Geometry

#### 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.

#### Solution

Construction:-

Steps of Construction:-

1. Construct an equilateral triangle Δ ABC with side 6 cm.
2. Draw perpendicular bisectors of any two sides. Let O be the point of intersection.
3. Draw a circle with centre O and radius OA or OB or OC. This gives us circumcircle equilateral triangle Δ ABC.
4. Draw the bisector of ∠C . It passes through centre of the circle O.
5. 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.

Is there an error in this question or solution?

#### APPEARS IN

2013-2014 (March) (with solutions)
Question 5.2 | 5.00 marks
Solution 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. Concept: Division of a Line Segment.
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