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AF, DE meet on median

Source: 10.1 of XX Geometrical Olympiad in honour of I.F.Sharygin

August 7, 2024
geogeometry

Problem Statement

The diagonals of a cyclic quadrilateral ABCDABCD meet at point PP. The bisector of angle ABDABD meets ACAC at point EE, and the bisector of angle ACDACD meets BDBD at point FF. Prove that the lines AFAF and DEDE meet on the median of triangle APDAPD.
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