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4 points lie on a circumference

Source: Rioplatense Olympiad 2013, Level 3, Problem 6

August 23, 2014

geometrycircumcircleparallelogram

Problem Statement

Let

ABC

be an acute scalene triangle,

H

its orthocenter and

G

its geocenter. The circumference with diameter

AH

cuts the circumcircle of

BHC

A'

(

A' \neq H

). Points

B'

and

C'

are defined similarly. Show that the points

A'

B'

C'

, and

G

lie in one circumference.