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ITAMO
2022 ITAMO
2
2
Part of
2022 ITAMO
Problems
(1)
Italian Mathematical Olympiad 2022 - Problem 2
Source:
5/6/2022
Let
A
B
C
ABC
A
BC
be an acute triangle with
A
B
<
A
C
AB<AC
A
B
<
A
C
. Let then •
D
D
D
be the foot of the bisector of the angle in
A
A
A
, •
E
E
E
be the point on segment
B
C
BC
BC
(different from
B
B
B
) such that
A
B
=
A
E
AB=AE
A
B
=
A
E
, •
F
F
F
be the point on segment
B
C
BC
BC
(different from
B
B
B
) such that
B
D
=
D
F
BD=DF
B
D
=
D
F
, •
G
G
G
be the point on segment
A
C
AC
A
C
such that
A
B
=
A
G
AB=AG
A
B
=
A
G
. Prove that the circumcircle of triangle
E
F
G
EFG
EFG
is tangent to line
A
C
AC
A
C
.
geometry