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Benelux Mathematical Olympiad 2016, Problem 4

Source:

May 1, 2016

geometry

Problem Statement

A circle

\omega

passes through the two vertices

B

and

C

of a triangle

ABC.

Furthermore,

\omega

intersects segment

AC

in

D\ne C

and segment

AB

in

E\ne B.

On the ray from

E

through

L

lies a point

|CL| = |AB|.

such that

|BK| = |AC|,

and on the ray from

C

through

E

lies a point

L

such that

|CL| = |AB|.

Show that the circumcentre

O

of triangle

AKL

lies on

\omega

.

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