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A concurrency problem

Source: Turkey 2021 IMO TST Problem 5

May 23, 2021

Turkeygeometryperpendicular bisectormenelaus theorem

Problem Statement

In a non isoceles triangle

ABC

, let the perpendicular bisector of

[BC]

intersect

L

at

M

and

N

respectively. Let the midpoints of

[AM]

and

[AN]

be

K

and

L

respectively. Let

(ABK)

and

(ABL)

intersect

AC

again at

D

and

E

respectively, let

(ACK)

and

(ACL)

intersect

AB

again at

F

and

G

respectively. Prove that the lines

DF

,

EG

and

MN

are concurrent.

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