MathDB

6

Part of 2023 Myanmar IMO Training

Problems(1)

Simple concyclic question

Source: Sharygin 2019 Finals Day 2 Grade 8 P7

7/31/2019
Let points MM and NN lie on sides ABAB and BCBC of triangle ABCABC in such a way that MN∣∣ACMN||AC. Points M′M' and N′N' are the reflections of MM and NN about BCBC and ABAB respectively. Let M′AM'A meet BCBC at XX, and let N′CN'C meet ABAB at YY. Prove that A,C,X,YA,C,X,Y are concyclic.
geometrySharygin Geometry Olympiad