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2016 Benelux
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4
Part of
2016 Benelux
Problems
(1)
Benelux Mathematical Olympiad 2016, Problem 4
Source:
5/1/2016
A circle
ω
\omega
ω
passes through the two vertices
B
B
B
and
C
C
C
of a triangle
A
B
C
.
ABC.
A
BC
.
Furthermore,
ω
\omega
ω
intersects segment
A
C
AC
A
C
in
D
≠
C
D\ne C
D
=
C
and segment
A
B
AB
A
B
in
E
≠
B
.
E\ne B.
E
=
B
.
On the ray from
B
B
B
through
D
D
D
lies a point
K
K
K
such that
∣
B
K
∣
=
∣
A
C
∣
,
|BK| = |AC|,
∣
B
K
∣
=
∣
A
C
∣
,
and on the ray from
C
C
C
through
E
E
E
lies a point
L
L
L
such that
∣
C
L
∣
=
∣
A
B
∣
.
|CL| = |AB|.
∣
C
L
∣
=
∣
A
B
∣.
Show that the circumcentre
O
O
O
of triangle
A
K
L
AKL
A
K
L
lies on
ω
\omega
ω
.
geometry