IMO 1995 — Shortlisted problems Question 8

G2 (GER). Let $A$, $B$, and $C$ be noncollinear points. Prove that there is a unique point $X$ in the plane of $ABC$ such that $XA^2+XB^2+AB^2=XB^2+XC^2+BC^2=XC^2+XA^2+CA^2$.