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The locus of the point equidistant (in a...

The locus of the point equidistant (in a plane) from the three vertices of a triangle is ____

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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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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.