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Portugal MO
2008 Portugal MO
2
2
Part of
2008 Portugal MO
Problems
(1)
Equivalence between sides - Portuguese MO, Problem 2, 2008
Source:
8/31/2010
Let
A
E
B
C
AEBC
A
EBC
be a cyclic quadrilateral. Let
D
D
D
be a point on the ray
A
E
AE
A
E
which is outside the circumscribed circumference of
A
E
B
C
AEBC
A
EBC
. Suppose that
∠
C
A
B
=
∠
B
A
E
\angle CAB=\angle BAE
∠
C
A
B
=
∠
B
A
E
. Prove that
A
B
=
B
D
AB=BD
A
B
=
B
D
if and only if
D
E
=
A
C
DE=AC
D
E
=
A
C
.
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geometry