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if triangles ABC and AMN are similar, then parallelogram ABCD is a square

Source: 2002 Romania JBMO TST1 p4

May 16, 2020
geometryparallelogramsquaresimilar trianglessimilar

Problem Statement

Let ABCDABCD be a parallelogram of center OO. Points MM and NN are the midpoints of BOBO and CDCD, respectively. Prove that if the triangles ABCABC and AMNAMN are similar, then ABCDABCD is a square.
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