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Problem 2 of Third round

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

December 14, 2019
geometry

Problem Statement

Let ABCDABCD be a quadrilateral, with an inscribed circle with center II. Through AA are constructed perpendiculars to ABAB and ADAD, which intersect BIBI and DIDI in points MM and NN respectively. Prove that MN⊥ACMN\perp AC.
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