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Equal angles in a parallelogram

Source: XVII Sharygin Correspondence Round P9

March 2, 2021
geometryparallelogram

Problem Statement

Points EE and FF lying on sides BCBC and ADAD respectively of a parallelogram ABCDABCD are such that EF=ED=DCEF=ED=DC. Let MM be the midpoint of BEBE and MDMD meet EFEF at GG. Prove that ∠EAC=∠GBD\angle EAC=\angle GBD.
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