A) Incentre of the triangle
B) Centroid of the triangle
C) Orthocentre of the triangle
D) None of these
Correct Answer: B
Solution :
Let a triangle has its three vertices as (0, 0), (a, 0), (0, b). We have the moving point (h, k) such that \[{{h}^{2}}+{{k}^{2}}+{{(h-a)}^{2}}+{{k}^{2}}+{{h}^{2}}+{{(k-b)}^{2}}=c\] \[\Rightarrow 3{{h}^{2}}+3{{k}^{2}}-2ah-2bk+{{a}^{2}}+{{b}^{2}}=c\] Therefore, \[3{{x}^{2}}+3{{y}^{2}}-2ax-2by+{{a}^{2}}+{{b}^{2}}=c\] Its centre is \[\left( \frac{a}{3},\ \frac{b}{3} \right)\], which is centroid of \[\Delta \].
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