MathDB
Prove this inequality for any point in the plane of triangle

Source: 2009 Jozsef Wildt International Math Competition

April 27, 2020
Trianglegeometryinequalities

Problem Statement

If KK, LL, MM denote the midpoints of the sides ABAB, BCBC, CACA in triangle △ABC\triangle ABC, then for all PP in the plane of triangle △ABC\triangle ABC, we have ABPK+BCPL+CAPM≥AB⋅BC⋅CA4⋅PK⋅PL⋅PM\frac{AB}{PK}+\frac{BC}{PL}+\frac{CA}{PM} \geq \frac{AB\cdot BC \cdot CA}{4\cdot PK\cdot PL\cdot PM}
Back to ProblemsView on AoPS