2004 USAMO Problems/Problem 6

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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.

Solution

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Resources

2004 USAMO (ProblemsResources)
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