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Perpendicular bisector meets the circumcircle of another triangle

Source: 2023 Junior Macedonian Mathematical Olympiad P4

June 10, 2023

geometry

Problem Statement

We are given an acute

\triangle ABC

with circumcenter

O

such that

BC<AB

. The bisector of

\angle ACB

meets the circumcircle of

\triangle ABC

at a second point

D

. The perpendicular bisector of

AC

meets the circumcircle of

\triangle BOD

for the second time at

E

. The line

DE

meets the circumcircle of

\triangle ABC

for the second time at

F

. Prove that the lines

CF

,

OE

and

AB

are concurrent.
Proposed by Petar Filipovski

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