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Geo with obtuse triangle

Source: Kazakhstan National MO 2023 (10-11).1

March 21, 2023

geometry

Problem Statement

A triangle

ABC

with obtuse angle

C

and

AC>BC

has center

O

of its circumcircle

\omega

. The tangent at

C

to

\omega

meets

AB

at

OF \cap CE=T

. Let

\Omega

be the circumcircle of

AOB

. Let

OD, AC

meet

\Omega

at

E, F

and let

OF \cap CE=T

,

OD \cap BC=K

. Prove that

OTBK

is cyclic.

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