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2009 ToT Spring Junior O P5 circumcenter lies on rhombus diagonal

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February 26, 2020
geometryrhombusCircumcenter

Problem Statement

In rhombus ABCDABCD, angle AA equals 120o120^o. Points MM and NN are chosen on sides BCBC and CDCD so that angle NAMNAM equals 30o30^o. Prove that the circumcenter of triangle NAMNAM lies on a diagonal of of the rhombus.
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