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Problems
Contests
National and Regional Contests
Serbia Contests
Serbia JBMO TST
2015 Junior Balkan Team Selection Test
4
4
Part of
2015 Junior Balkan Team Selection Test
Problems
(1)
Serbia Junior Balkan TST 2015
Source:
5/25/2015
The diagonals
A
D
AD
A
D
,
B
E
BE
BE
,
C
F
CF
CF
of cyclic hexagon
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
intersect in
S
S
S
and
A
B
AB
A
B
is parallel to
C
F
CF
CF
and lines
D
E
DE
D
E
and
C
F
CF
CF
intersect each other in
M
M
M
. Let
N
N
N
be a point such that
M
M
M
is the midpoint of
S
N
SN
SN
. Prove that circumcircle of
△
A
D
N
\triangle ADN
△
A
D
N
is passing through midpoint of segment
C
F
CF
CF
.
geometry