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2015 Balkan MO Shortlist
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Part of
2015 Balkan MO Shortlist
Problems
(1)
2015 Bulgaria Team Selection Test Round 1, Problem 2
Source:
9/17/2015
Quadrilateral
A
B
C
D
ABCD
A
BC
D
is given with
A
D
∦
B
C
AD \nparallel BC
A
D
∦
BC
. The midpoints of
A
D
AD
A
D
and
B
C
BC
BC
are denoted by
M
M
M
and
N
N
N
, respectively. The line
M
N
MN
MN
intersects the diagonals
A
C
AC
A
C
and
B
D
BD
B
D
in points
K
K
K
and
L
L
L
, respectively. Prove that the circumcircles of the triangles
A
K
M
AKM
A
K
M
and
B
N
L
BNL
BN
L
have common point on the line
A
B
AB
A
B
.( Proposed by Emil Stoyanov ) http://estoyanov.net/wp-content/uploads/2015/09/est.png
geometry
circumcircle