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Prove that the locus of the point that m...

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

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Let vertices of triangle are (0,0), (a,0) and (b,c).
The variable point (x,y) is such that
`(x-o)^(2)+(y-0)^(2)+(x-a)^(2)+(y-0)^(2)+(x-b)^(2)+(y-c)^(2)=lambda`(constant)
`:. 3x^(2)_3y^(2)-2(a+b)x-2cy+a^(2)+b^(2)+c^(2)-lambda=0`, which is equation of circle.
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