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Singapore Senior Math Olympiad
2019 Singapore Senior Math Olympiad
1
1
Part of
2019 Singapore Senior Math Olympiad
Problems
(1)
Angle Bisector in a Parallelogram
Source: SMO Senior 2019 Q1
6/29/2019
In a parallelogram
A
B
C
D
ABCD
A
BC
D
, the bisector of
∠
A
\angle A
∠
A
intersects
B
C
BC
BC
at
M
M
M
and the extension of
D
C
DC
D
C
at
N
N
N
. Let
O
O
O
be the circumcircle of the triangle
M
C
N
MCN
MCN
. Prove that
∠
O
B
C
=
∠
O
D
C
\angle OBC = \angle ODC
∠
OBC
=
∠
O
D
C
geometry
angle bisector
parallelogram
circumcircle