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Question

In an equilateral triangle, centroid and the circumcentre coincide.



Correct Answer
A

True

Your Answer
B

False


Solution

The correct option is A

True


Consider an equilateral triangle ABC inscribed in a circle.
Let O be the circumcentre.
Then OA = OB = OC    - - -(1) 

Draw three medians AD, BE and CF intersecting at G. Then G is the centroid of ABC.

In BFC and CEB, 

BC = BC; B = C = 60; BF = CE (since AB = AC)

BFC CEB

BE = CF, similarly, AD = BE

Thus AD = BE = CF

23AD=23BE=23CF

GA = GB = GC    - - -(2) ( the centroid divides each median in the ratio 2:1)

Hence, from (1) and (2), we can conclude that G coincides with O.

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