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2020 IMO Shortlist
G3
G3
Part of
2020 IMO Shortlist
Problems
(1)
geometry with quadrilateral, tangent circles wanted
Source: IMO 2020 Shortlist G3
7/20/2021
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral with
∠
A
B
C
>
90
\angle ABC>90
∠
A
BC
>
90
,
C
D
A
>
90
CDA>90
C
D
A
>
90
and
∠
D
A
B
=
∠
B
C
D
\angle DAB=\angle BCD
∠
D
A
B
=
∠
BC
D
. Denote by
E
E
E
and
F
F
F
the reflections of
A
A
A
in lines
B
C
BC
BC
and
C
D
CD
C
D
, respectively. Suppose that the segments
A
E
AE
A
E
and
A
F
AF
A
F
meet the line
B
D
BD
B
D
at
K
K
K
and
L
L
L
, respectively. Prove that the circumcircles of triangles
B
E
K
BEK
BE
K
and
D
F
L
DFL
D
F
L
are tangent to each other.\emph{Slovakia}
geometry
IMO Shortlist