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Croatian mathematical olympiad, day 1 problem 3

Source:

April 10, 2011

geometrycircumcircleratiogeometric transformationhomothetygeometry unsolved

Problem Statement

Triangle

ABC

is given with its centroid

G

and cicumcentre

O

is such that

GO

is perpendicular to

AG

. Let

A'

be the second intersection of

AG

with circumcircle of triangle

ABC

. Let

D

be the intersection of lines

CA'

and

AB

and

E

the intersection of lines

BA'

and

AC

. Prove that the circumcentre of triangle

ADE

is on the circumcircle of triangle

ABC

.

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