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International Contests
Mathematical Excellence Olympiad
2017 IMEO
2
2
Part of
2017 IMEO
Problems
(1)
IMEO 2017 Problem 2
Source: IMEO
9/28/2017
Let
O
O
O
be the circumcenter of a triangle
A
B
C
ABC
A
BC
. Let
M
M
M
be the midpoint of
A
O
AO
A
O
. The
B
O
BO
BO
and
C
O
CO
CO
intersect the altitude
A
D
AD
A
D
at points
E
E
E
and
F
F
F
,respectively. Let
O
1
O1
O
1
and
O
2
O2
O
2
be the circumcenters of the triangle ABE and
A
C
F
ACF
A
CF
, respectively. Prove that M lies on
O
1
O
2
O1O2
O
1
O
2
.
geometry
Junior