Question

The locus of point which moves such that sum of squares of distance from 3 vertices of triangle is constant. What is the center of the circle?

Answer 1

This is a pretty confusing one most definitely, and I'm not sure if it's answerable without knowing some coordinates. What I think it happening is:

\[a_1^2+b_1^2+c_1^2=a_2^2+b_2^2+c_2^2=a_3^2+b_3^2+c_3^2=a_n^2+b_n^2+c_n^2=k\]Without being able to discern what those distances are numerically, I don't see a way to actually calculate the center (considering that it could be anywhere in space, regardless of the actual values.

I can only imagine that it's a theory question, and you're meant to realise that it's the circumcentre, or the incentre, or centroid of the triangle, or something like that.