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2019 JBMO Shortlist
G3
G3
Part of
2019 JBMO Shortlist
Problems
(1)
JBMO Shortlist 2019 G3
Source:
9/12/2020
Let
A
B
C
ABC
A
BC
be a triangle with incenter
I
I
I
. The points
D
D
D
and
E
E
E
lie on the segments
C
A
CA
C
A
and
B
C
BC
BC
respectively, such that
C
D
=
C
E
CD = CE
C
D
=
CE
. Let
F
F
F
be a point on the segment
C
D
CD
C
D
. Prove that the quadrilateral
A
B
E
F
ABEF
A
BEF
is circumscribable if and only if the quadrilateral
D
I
E
F
DIEF
D
I
EF
is cyclic.Proposed by Dorlir Ahmeti, Albania
geometry