MathDB
Inequality in an isosceles triangle

Source: INMO 2007 Question 5

November 2, 2009
inequalitiesgeometry unsolvedgeometry

Problem Statement

Let ABC ABC be a triangle in which AB\equal{}AC. Let D D be the midpoint of BC BC and P P be a point on AD AD. Suppose E E is the foot of perpendicular from P P on AC AC. Define \frac{AP}{PD}\equal{}\frac{BP}{PE}\equal{}\lambda , \ \ \ \frac{BD}{AD}\equal{}m , \ \ \ z\equal{}m^2(1\plus{}\lambda) Prove that z^2 \minus{} (\lambda^3 \minus{} \lambda^2 \minus{} 2)z \plus{} 1 \equal{} 0 Hence show that λ≥2 \lambda \ge 2 and \lambda \equal{} 2 if and only if ABC ABC is equilateral.
Back to ProblemsView on AoPS