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National and Regional Contests
Italy Contests
ITAMO
2010 ITAMO
3
3
Part of
2010 ITAMO
Problems
(1)
angle BCM=angle DBA in a convex quad
Source: ItaMO 2010, p3
2/28/2012
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral. such that
∠
C
A
B
=
∠
C
D
A
\angle CAB = \angle CDA
∠
C
A
B
=
∠
C
D
A
and
∠
B
C
A
=
∠
A
C
D
\angle BCA = \angle ACD
∠
BC
A
=
∠
A
C
D
. If
M
M
M
be the midpoint of
A
B
AB
A
B
, prove that
∠
B
C
M
=
∠
D
B
A
\angle BCM = \angle DBA
∠
BCM
=
∠
D
B
A
.
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