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National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2023 Junior Balkan Team Selection Tests - Moldova
8
8
Part of
2023 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
Prove that the angles $AMP$ and $BMN$ are equal.
Source: Moldova JTST 2023
5/5/2023
Let
A
B
C
D
ABCD
A
BC
D
be a trapezoid with bases
A
B
AB
A
B
and
C
D
CD
C
D
(
A
B
>
C
D
)
(AB>CD)
(
A
B
>
C
D
)
. Diagonals
A
C
AC
A
C
and
B
D
BD
B
D
intersect in point
N
N
N
and lines
A
D
AD
A
D
and
B
C
BC
BC
intersect in point
M
M
M
. The circumscribed circles of
A
D
N
ADN
A
D
N
and
B
C
N
BCN
BCN
intersect in point
P
P
P
, different from point
N
N
N
. Prove that the angles
A
M
P
AMP
A
MP
and
B
M
N
BMN
BMN
are equal.
geometry
trapezoid