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Three points on the sides of triangle ABC imply inequality

Source: Balkan MO 1992, Problem 3

April 25, 2006
inequalitiesgeometrycircumcircletrigonometrygeometry proposed

Problem Statement

Let DD, EE, FF be points on the sides BCBC, CACA, ABAB respectively of a triangle ABCABC (distinct from the vertices). If the quadrilateral AFDEAFDE is cyclic, prove that 4A[DEF]A[ABC]≤(EFAD)2. \frac{ 4 \mathcal A[DEF] }{\mathcal A[ABC] } \leq \left( \frac{EF}{AD} \right)^2 . Greece
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