prove that the centre of a circle coincides with the centroid of an equilateral triangle inscribed in it
Asked by Tejas Kulkarni | 14th Feb, 2014, 02:06: PM
Given: An equilateral triangle ABC in which D,E and F are the mid-points of the sides BC,CA and AB respectively.
To Prove: The centroid and the ircumcenter coinsident.
Construction: Draw medians AD, BE and CF.
Proof: Let G be the centroid of ABC i.e. the point of intersection of AD, BE and CF.
In BCE and BFC, we have
and, BF=CE (since AB=ACAB=ACBF=CE)
Similarly, CAF CAD
From (i) and (ii) we get,
G is equidistance from vertices
G is the circumcenter of ABC
Hence, the centroid and circumcenter are cincident.
Answered by | 14th Feb, 2014, 06:15: PM
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