1996 USAMO Problems/Problem 3
Problem
Let be a triangle. Prove that there is a line (in the plane of triangle ) such that the intersection of the interior of triangle and the interior of its reflection in has area more than the area of triangle .
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.