MathDB
Problem 1, Geometric Inequality

Source: Danube Contest 2016, Romania

October 29, 2017
geometric inequalityinequalities

Problem Statement

1.Let ABCABC be a triangle, DD the foot of the altitude from AA and MM the midpoint of the side BCBC. Let SS be a point on the closed segment DMDM and let P,QP, Q the projections of SS on the lines ABAB and ACAC respectively. Prove that the length of the segment PQPQ does not exceed one quarter the perimeter of the triangle ABCABC.
Back to ProblemsView on AoPS