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Simple concyclic question

Source: Sharygin 2019 Finals Day 2 Grade 8 P7

July 31, 2019

geometrySharygin Geometry Olympiad

Problem Statement

Let points

M

and

N

lie on sides

AB

and

BC

of triangle

ABC

in such a way that

MN||AC

. Points

M'A

and

N'

are the reflections of

M

and

N

about

BC

and

AB

respectively. Let

M'A

meet

BC

at

X

, and let

N'C

meet

AB

at

Y

. Prove that

A,C,X,Y

are concyclic.

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