MathDB
min |BL|^2 + |CM|^2 + |AN|^2

Source: Polish MO Recond Round 1988 p3

September 9, 2024
geometryGeometric Inequalities

Problem Statement

Inside the acute-angled triangle ABC ABC we consider the point P P and its projections L,M,N L, M, N to the sides BC,CA,AB BC, CA, AB , respectively. Determine the point P P for which the sum ∣BL∣2+∣CM∣2+∣AN∣2 |BL|^2 + |CM|^2 + |AN|^2 is the smallest.
Back to ProblemsView on AoPS