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Problems
Contests
International Contests
Baltic Way
1998 Baltic Way
13
13
Part of
1998 Baltic Way
Problems
(1)
pentagon
Source: Baltic Way 1998
6/28/2009
In convex pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
, the sides
A
E
,
B
C
AE,BC
A
E
,
BC
are parallel and
∠
A
D
E
=
∠
B
D
C
\angle ADE=\angle BDC
∠
A
D
E
=
∠
B
D
C
. The diagonals
A
C
AC
A
C
and
B
E
BE
BE
intersect at
P
P
P
. Prove that
∠
E
A
D
=
∠
B
D
P
\angle EAD=\angle BDP
∠
E
A
D
=
∠
B
D
P
and
∠
C
B
D
=
∠
A
D
P
\angle CBD=\angle ADP
∠
CB
D
=
∠
A
D
P
.
geometry proposed
geometry