MathDB
Identify U

Source: IMO Longlist 1989, Problem 23

September 18, 2008
geometry unsolvedgeometry

Problem Statement

Let ABC ABC be a triangle. Prove that there is a unique point U U in the plane of ABC ABC such that there exist real numbers α,β,γ,δ \alpha, \beta, \gamma, \delta not all zero, such that \alpha PL^2 \plus{} \beta PM^2 \plus{} \gamma PN^2 \plus{} \delta UP^2 is constant for all points P P of the plane, where L,M,N L,M,N are the feet of the perpendiculars from P P to BC,CA,AB BC,CA,AB respectively. Identify U. U.
Back to ProblemsView on AoPS