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.