Prove that the locus of a point which moves such that the sum of the square of its distances from the vertices of a triangle is constant is a circle having centre at the centroid of the triangle.

Options

A. centroid of triangle ABC
B. circumcentre of `DeltaABC`
C. orthocentre of `DeltaABC`
D. none of these

Answer

A

Explanation

As discussed in the above example that the centre of the circle is
`((x_(1)+x_(2)+x_(3))/(3), (y_(1)+y_(2)+y_(3))/(3))`, which is the centroid of `DeltaABC`.