2004 USAMO Problems/Problem 6

Problem

A circle $\omega$ is inscribed in a quadrilateral $ABCD$ . Let $I$ be the center of $\omega$ . Suppose that

$(AI + DI)^2 + (BI + CI)^2 = (AB + CD)^2$ .

Prove that $ABCD$ is an isosceles trapezoid.

2004 USAMO (Problems • Resources)
Preceded by Problem 5	Followed by Last problem
1 • 2 • 3 • 4 • 5 • 6
All USAMO Problems and Solutions