CBSE Class 9 Answered
prove that the centre of a circle coincides with the centroid of an equilateral triangle inscribed in it
Asked by Tejas Kulkarni | 14 Feb, 2014, 02:06: PM
Expert Answer
Dear Student,
Soln:
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
B=C=60o,
BC=BC
and, BF=CE (since AB=ACAB=ACBF=CE)
BCE BFC
BE=CF ....(i)
Similarly, CAF CAD
CF=AD ........(ii)
From (i) and (ii) we get,
AB=BE=CF
AD=BE=CF
GA=GB=GC
G is equidistance from vertices
G is the circumcenter of ABC
Hence, the centroid and circumcenter are cincident.
Answered by | 14 Feb, 2014, 06:15: PM
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