6

Part of 2013 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

4 points lie on a circumference

Source: Rioplatense Olympiad 2013, Level 3, Problem 6

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

B'

C'

are defined similarly. Show that the points

A'

B'

C'

G

lie in one circumference.

geometrycircumcircleparallelogram