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National and Regional Contests
Greece Contests
Greece JBMO TST
2023 Greece JBMO TST
2
2
Part of
2023 Greece JBMO TST
Problems
(1)
Equal segments in a cyclic quadrilateral
Source: Greece JBMO TST 2023 P2
7/29/2023
Consider a cyclic quadrilateral
A
B
C
D
ABCD
A
BC
D
in which
B
C
=
C
D
BC = CD
BC
=
C
D
and
A
B
<
A
D
AB < AD
A
B
<
A
D
. Let
E
E
E
be a point on the side
A
D
AD
A
D
and
F
F
F
a point on the line
B
C
BC
BC
such that
A
E
=
A
B
=
A
F
AE = AB = AF
A
E
=
A
B
=
A
F
. Prove that
E
F
∥
B
D
EF \parallel BD
EF
∥
B
D
.
geometry
cyclic quadrilateral