MathDB
Intersections

Source: USAMO 1996

October 22, 2005
geometrygeometric transformationreflectiontrapezoidinequalitiesratioangle bisector

Problem Statement

Let ABCABC be a triangle. Prove that there is a line ℓ\ell (in the plane of triangle ABCABC) such that the intersection of the interior of triangle ABCABC and the interior of its reflection A′B′C′A'B'C' in ℓ\ell has area more than 23\frac23 the area of triangle ABCABC.
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