2004 USAMO Problems/Problem 6: Difference between revisions

Revision as of 13:51, 8 April 2013

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.

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2004 USAMO (Problems • Resources)
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