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South East Mathematical Olympiad
2009 South East Mathematical Olympiad
2
Convex pentagon - A, B, C, D are concyclic
Convex pentagon - A, B, C, D are concyclic
Source:
September 18, 2010
geometry
trapezoid
circumcircle
geometry proposed
Problem Statement
In the convex pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
we know that
A
B
=
D
E
,
B
C
=
E
A
AB=DE, BC=EA
A
B
=
D
E
,
BC
=
E
A
but
A
B
≠
E
A
AB \neq EA
A
B
=
E
A
.
B
,
C
,
D
,
E
B,C,D,E
B
,
C
,
D
,
E
are concyclic . Prove that
A
,
B
,
C
,
D
A,B,C,D
A
,
B
,
C
,
D
are concyclic if and only if
A
C
=
A
D
.
AC=AD.
A
C
=
A
D
.
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