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Iran geometry

Source: Iran MO 3rd round 2019 mid-terms - Geometry P2

August 2, 2019

geometrycircumcircle

Problem Statement

Consider an acute-angled triangle

ABC

with

AB=AC

and

\angle A>60^\circ

. Let

O

be the circumcenter of

ABC

. Point

P

lies on circumcircle of

BOC

such that

BP\parallel AC

and point

K

lies on segment

AP

such that

BK=BC

. Prove that

CK

bisects the arc

BC

of circumcircle of

BOC

.

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