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Concurrent circles in incircle structure

Source: Iran MO second round 2024 P3

April 18, 2024

geometryincenter

Problem Statement

In a triangle

ABC

the incenter, the

B

-excenter and the

C

-excenter are

E

and

L

, respectively. The perpendiculars at

B

and

C

to

BC

intersect the lines

AC

and

AB

at

E

and

F

, respectively. Prove that the circumcircles of

AEF, FIL, EIK

concur.

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