1996 USAMO Problems/Problem 3

Problem

Let $ABC$ be a triangle. Prove that there is a line $l$ (in the plane of triangle $ABC$ ) such that the intersection of the interior of triangle $ABC$ and the interior of its reflection $A'B'C'$ in $l$ has area more than $\frac{2}{3}$ the area of triangle $ABC$ .

Hint

Without loss of generality, set A(0,0), B(a,1), and C(b,1). The line of reflection should be y = k for some constant k.

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1996 USAMO Problems/Problem 3

Problem

Hint