MathDB
Problems
Contests
International Contests
IMO Shortlist
2017 IMO Shortlist
G1
G1
Part of
2017 IMO Shortlist
Problems
(1)
Shortlist 2017/G1
Source: Shortlist 2017
7/10/2018
Let
A
B
C
D
E
ABCDE
A
BC
D
E
be a convex pentagon such that
A
B
=
B
C
=
C
D
AB=BC=CD
A
B
=
BC
=
C
D
,
∠
E
A
B
=
∠
B
C
D
\angle{EAB}=\angle{BCD}
∠
E
A
B
=
∠
BC
D
, and
∠
E
D
C
=
∠
C
B
A
\angle{EDC}=\angle{CBA}
∠
E
D
C
=
∠
CB
A
. Prove that the perpendicular line from
E
E
E
to
B
C
BC
BC
and the line segments
A
C
AC
A
C
and
B
D
BD
B
D
are concurrent.
geometry
IMO Shortlist
pentagon
Inscribed circle