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China South East Mathematical Olympiad 2021 Grade11 P6

Source:

July 30, 2021
geometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral. The internal angle bisector of ∠BAD\angle BAD and line BCBC intersect at E.E. MM is the midpoint of segment AE.AE. The exterior angle bisector of ∠BCD\angle BCD and line ADAD intersect at F.F. The lines MFMF and ABAB intersect at G.G. Prove that if AB=2AD,AB=2AD, then MF=2MG.MF=2MG.
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