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DE-MO 2007 Problem 3

    We say that two triangles are oriented similarly if they are similar and have the same orientation. Prove that if ALT,ARM,ORT,ALT, ARM, ORT, and ULMULM are four triangles which are oriented similarly, then AA is the midpoint of the line segment OU.OU.

    Dataset text AI-MO AoPS. Quoted with source.

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