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Saint Petersburg Mathematical Olympiad
2015 Saint Petersburg Mathematical Olympiad
2
Trapezoid geometry
Trapezoid geometry
Source: St Petersburg Olympiad 2015, Grade 9, P2
October 17, 2017
geometry
circumcircle
trapezoid
Problem Statement
A
B
=
C
D
,
A
D
∥
B
C
AB=CD,AD \parallel BC
A
B
=
C
D
,
A
D
∥
BC
and
A
D
>
B
C
AD>BC
A
D
>
BC
.
Ω
\Omega
Ω
is circumcircle of
A
B
C
D
ABCD
A
BC
D
. Point
E
E
E
is on
Ω
\Omega
Ω
such that
B
E
⊥
A
D
BE \perp AD
BE
⊥
A
D
. Prove that
A
E
+
B
C
>
D
E
AE+BC>DE
A
E
+
BC
>
D
E
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