1976 AMC 12 Question 22 - thichhoctoan.com

Question 22

Given an equilateral triangle with side of length $s,$ consider the locus of all points $P$ in the plane of the triangle such that the sum of the squares of the distances from $P$ to the vertices of the triangle is a fixed number $a.$ This locus

is a circle if $a\gt s^2$
contains only three points if $a=2s^2$ and is a circle if
$a\gt2s^2$
is a circle with positive radius only if $s^2\lt
a\lt2s^2$
contains only a finite number of points for any value of
$a$
is none of these