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Nice geometry in Iran.

Source: Iranian Third Round 2020 Geometry exam Problem2

November 18, 2020

geometry

Problem Statement

Triangle

ABC

with it's circumcircle

\Gamma

is given. Points

D

and

E

are chosen on segment

BC

such that

\angle BAD=\angle CAE

. The circle

\omega

is tangent to

AD

at

A

with it's circumcenter lies on

\Gamma

. Reflection of

A

through

BC

is

A'

. If the line

A'E

meet

\omega

at

L

and

K

. Then prove either

BL

and

CK

or

BK

and

CL

meet on

\Gamma

.

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