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Saint Petersburg Mathematical Olympiad
2001 Saint Petersburg Mathematical Olympiad
9.3
9.3
Part of
2001 Saint Petersburg Mathematical Olympiad
Problems
(1)
On a circumscribed pentagon
Source: St. Petersburg MO 2001 Grade 9 Problem 3
3/1/2023
A convex pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
is given with
A
B
=
B
C
AB=BC
A
B
=
BC
,
C
D
=
D
E
CD=DE
C
D
=
D
E
and
∠
A
=
∠
C
=
∠
E
>
9
0
∘
\angle A=\angle C=\angle E>90^{\circ}
∠
A
=
∠
C
=
∠
E
>
9
0
∘
. Prove that the pentagon is circumscribed[I]Proposed by F. Baharev
geometry
St. Petersburg MO
pentagon
circumscribed