MathDB

Geometry with Miquel configuration

Source: 2024 Turkey EGMO TST P1

February 12, 2024

geometrycircumcircleincentre

Problem Statement

Let

ABC

be a triangle and its circumcircle be

\omega

. Let

I

be the incentre of the

ABC

. Let the line

BI

meet

AC

at

E

and

\omega

at

M

for the second time. The line

CI

meet

AB

at

F

and

\omega

at

N

for the second time. Let the circumcircles of

BFI

and

CEI

meet again at point

K

. Prove that the lines

BN

,

CM

,

AK

are concurrent.

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