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Lusophon Mathematical Olympiad
2019 Lusophon Mathematical Olympiad
3
3
Part of
2019 Lusophon Mathematical Olympiad
Problems
(1)
IG // AB iff CI // IO
Source: Lusophon 2019 CPLP P3
12/31/2019
Let
A
B
C
ABC
A
BC
be a triangle with
A
C
≠
B
C
AC \ne BC
A
C
=
BC
. In triangle
A
B
C
ABC
A
BC
, let
G
G
G
be the centroid,
I
I
I
the incenter and O Its circumcenter. Prove that
I
G
IG
I
G
is parallel to
A
B
AB
A
B
if, and only if,
C
I
CI
C
I
is perpendicular on
I
O
IO
I
O
.
geometry
parallel
perpendicular