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Concurrency of BC, OI, AK

Source: own, Iran MO 3rd round 2019 mid-terms - Geometry P3

July 31, 2019

geometrycircumcircleincenter

Problem Statement

Consider a triangle

ABC

with circumcenter

O

and incenter

I

. Incircle touches sides

BC,CA

and

AB

D, E

and

F

K

is a point such that

KF

is tangent to circumcircle of

BFD

and

KE

is tangent to circumcircle of

CED

. Prove that

BC,OI

and

AK

are concurrent.