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Junior Balkan Mathematical Olympiad 2021- P3

Source: JBMO 2021

July 1, 2021

JuniorBalkangeometrycircumcircleconcurrence

Problem Statement

Let

ABC

be an acute scalene triangle with circumcenter

O

. Let

D

be the foot of the altitude from

A

to the side

BC

. The lines

BC

and

AO

intersect at

E

. Let

s

be the line through

E

perpendicular to

AO

. The line

s

intersects

\omega

and

AC

at

K

and

L

, respectively. Denote by

\omega

the circumcircle of triangle

AKL

. Line

AD

intersects

\omega

again at

X

. Prove that

\omega

and the circumcircles of triangles

ABC

and

DEX

have a common point.

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