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Bangladesh Mathematical Olympiad
2013 Bangladesh Mathematical Olympiad
1
1
Part of
2013 Bangladesh Mathematical Olympiad
Problems
(1)
Degenerate Pentagon
Source: Bangladesh National MO 2013
3/5/2019
Higher Secondary P1A polygon is called degenerate if one of its vertices falls on a line that joins its neighboring two vertices. In a pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
,
A
B
=
A
E
AB=AE
A
B
=
A
E
,
B
C
=
D
E
BC=DE
BC
=
D
E
,
P
P
P
and
Q
Q
Q
are midpoints of
A
E
AE
A
E
and
A
B
AB
A
B
respectively.
P
Q
∣
∣
C
D
PQ||CD
PQ
∣∣
C
D
,
B
D
BD
B
D
is perpendicular to both
A
B
AB
A
B
and
D
E
DE
D
E
. Prove that
A
B
C
D
E
ABCDE
A
BC
D
E
is a degenerate pentagon.
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