MathDB

Unique point X

Source: IMO Shortlist 1995, G

August 3, 2008

geometrycircumcirclereflectioncomplex numbersperpendicular bisectorIMO Shortlist

Problem Statement

Let

A, B

and

C

be non-collinear points. Prove that there is a unique point

X

in the plane of

ABC

such that XA^2 \plus{} XB^2 \plus{} AB^2 \equal{} XB^2 \plus{} XC^2 \plus{} BC^2 \equal{} XC^2 \plus{} XA^2 \plus{} CA^2.