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Serbia Contests
Serbia National Math Olympiad
2014 Serbia National Math Olympiad
2
2
Part of
2014 Serbia National Math Olympiad
Problems
(1)
SMO 2014
Source:
5/22/2015
On sides
B
C
BC
BC
and
A
C
AC
A
C
of
△
A
B
C
\triangle ABC
△
A
BC
given are
D
D
D
and
E
E
E
, respectively. Let
F
F
F
(
F
≠
C
F \neq C
F
=
C
) be a point of intersection of circumcircle of
△
C
E
D
\triangle CED
△
CE
D
and line that is parallel to
A
B
AB
A
B
and passing through C. Let
G
G
G
be a point of intersection of line
F
D
FD
F
D
and side
A
B
AB
A
B
, and let
H
H
H
be on line
A
B
AB
A
B
such that
∠
H
D
A
=
∠
G
E
B
\angle HDA = \angle GEB
∠
HD
A
=
∠
GEB
and
H
−
A
−
B
H-A-B
H
−
A
−
B
. If
D
G
=
E
H
DG=EH
D
G
=
E
H
, prove that point of intersection of
A
D
AD
A
D
and
B
E
BE
BE
lie on angle bisector of
∠
A
C
B
\angle ACB
∠
A
CB
.Proposed by Milos Milosavljevic
geometry