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Circle through A of parallelogram ABCD

Source: Baltic Way 2001

November 17, 2010
geometryparallelogramgeometry proposed

Problem Statement

Given a parallelogram ABCDABCD. A circle passing through AA meets the line segments AB,ACAB, AC and ADAD at inner points M,K,NM,K,N, respectively. Prove that ∣AB∣⋅∣AM∣+∣AD∣⋅∣AN∣=∣AK∣⋅∣AC∣|AB|\cdot |AM | + |AD|\cdot |AN|=|AK|\cdot |AC|
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