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Balkan MO
2018 Balkan MO
1
1
Part of
2018 Balkan MO
Problems
(1)
Balkan Mathematical Olympiad 2018 P1
Source: BMO 2018
5/9/2018
A quadrilateral
A
B
C
D
ABCD
A
BC
D
is inscribed in a circle
k
k
k
where
A
B
AB
A
B
>
>
>
C
D
CD
C
D
,and
A
B
AB
A
B
is not paralel to
C
D
CD
C
D
.Point
M
M
M
is the intersection of diagonals
A
C
AC
A
C
and
B
D
BD
B
D
, and the perpendicular from
M
M
M
to
A
B
AB
A
B
intersects the segment
A
B
AB
A
B
at a point
E
E
E
.If
E
M
EM
EM
bisects the angle
C
E
D
CED
CE
D
prove that
A
B
AB
A
B
is diameter of
k
k
k
. Proposed by Emil Stoyanov,Bulgaria