MathDB

10.1

Part of 2024 Sharygin Geometry Olympiad

Problems(1)

AF, DE meet on median

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

8/7/2024
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.
geogeometry