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2022 IMO Shortlist
G7
G7
Part of
2022 IMO Shortlist
Problems
(1)
Triangles with same orthocenter and circumcircle
Source: 2022 G7
7/9/2023
Two triangles
A
B
C
,
A
’
B
’
C
’
ABC, A’B’C’
A
BC
,
A
’
B
’
C
’
have the same orthocenter
H
H
H
and the same circumcircle with center
O
O
O
. Letting
P
Q
R
PQR
PQR
be the triangle formed by
A
A
’
,
B
B
’
,
C
C
’
AA’, BB’, CC’
AA
’
,
BB
’
,
CC
’
, prove that the circumcenter of
P
Q
R
PQR
PQR
lies on
O
H
OH
O
H
.
Euler
geometry
circumcircle