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2020-IMOC
G3
G3
Part of
2020-IMOC
Problems
(1)
IMOC 2020 G3 (circumcenter of OM_BM_C lies on Euler line of BIC)
Source: https://artofproblemsolving.com/community/c6h2254883p17398793
9/1/2020
Triangle
A
B
C
ABC
A
BC
has incenter
I
I
I
and circumcenter
O
O
O
.
A
I
,
B
I
,
C
I
AI, BI, CI
A
I
,
B
I
,
C
I
intersect the circumcircle of
A
B
C
ABC
A
BC
again at
M
A
,
M
B
,
M
C
M_A, M_B, M_C
M
A
,
M
B
,
M
C
, respectively. Show that the Euler line of
B
I
C
BIC
B
I
C
passes through the circumcenter of
O
M
B
M
C
OM_BM_C
O
M
B
M
C
.(houkai)
geometry
circumcircle
Euler Line
incenter