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Nepal Contests
Nepal National Olympiad
2018 Nepal National Olympiad
3c
3c
Part of
2018 Nepal National Olympiad
Problems
(1)
Convex Pentagon
Source: Nepal Mathematics Olympiad
4/22/2018
Problem Section #3c) Let
A
B
C
D
E
ABCDE
A
BC
D
E
be a convex pentagon such that
B
C
∥
A
E
,
A
B
=
B
C
+
A
E
BC \parallel AE, AB = BC + AE
BC
∥
A
E
,
A
B
=
BC
+
A
E
, and
∠
A
B
C
=
∠
C
D
E
\angle{ABC} =\angle{CDE}
∠
A
BC
=
∠
C
D
E
. Let
M
M
M
be the midpoint of
C
E
CE
CE
, and let
O
O
O
be the circumcenter of triangle
B
C
D
BCD
BC
D
. Given that
∠
D
M
O
=
9
0
o
\angle{DMO}=90^{o}
∠
D
MO
=
9
0
o
, prove that
2
∠
B
D
A
=
∠
C
D
E
2\angle{BDA} =\angle{CDE}
2∠
B
D
A
=
∠
C
D
E
.
geometry