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National and Regional Contests
Hungary Contests
Kürschák Math Competition
1977 Kurschak Competition
2
2
Part of
1977 Kurschak Competition
Problems
(1)
concyclic wanted
Source: 1977 Hungary - Kürschák Competition p2
10/15/2022
A
B
C
ABC
A
BC
is a triangle with orthocenter
H
H
H
. The median from
A
A
A
meets the circumcircle again at
A
1
A_1
A
1
, and
A
2
A_2
A
2
is the reflection of
A
1
A_1
A
1
in the midpoint of
B
C
BC
BC
. The points
B
2
B_2
B
2
and
C
2
C_2
C
2
are defined similarly. Show that
H
H
H
,
A
2
A_2
A
2
,
B
2
B_2
B
2
and
C
2
C_2
C
2
lie on a circle. https://cdn.artofproblemsolving.com/attachments/f/1/192d14a0a7a9aa9ac7b38763e6ea6a4a95be55.png
geometry
Concyclic