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cyclic quadrilateral ABCD

Source: Iran TST 2023 ; Exam 1 Problem 2

March 15, 2023

geometrycyclic quadrilateralcircumcircle

Problem Statement

ABCD

is cyclic quadrilateral and

O

is the center of its circumcircle. Suppose that

BD

and

AC \cap BD = F

. Circle

\omega

is tanget to line

AC

and

BD

.

PQ

is a diameter of

\omega

that

F

is orthocenter of

EPQ

. Prove that line

OE

is passing through center of

\omega

Proposed by Mahdi Etesami Fard

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