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Korea Junior Mathematics Olympiad
1998 Korea Junior Math Olympiad
3
3
Part of
1998 Korea Junior Math Olympiad
Problems
(1)
KJMO 1998 P3 Homothety on orthocenter
Source: 1998 KJMO
6/30/2024
O
O
O
is the circumcenter of
A
B
C
ABC
A
BC
, and
H
H
H
is the orthocenter of
A
B
C
ABC
A
BC
. If
D
D
D
is a midpoint of
A
C
AC
A
C
and
E
E
E
is the intersection of
B
O
BO
BO
and
A
B
C
ABC
A
BC
's circumcircle not
B
B
B
, show that three points
H
,
D
,
E
H, D, E
H
,
D
,
E
are collinear.
geometry
circumcircle
homothety
geometric transformation