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Weird configuration geometry

Source: Indonesia TSTST - Geometry

February 29, 2024

geometry

Problem Statement

Given a concyclic quadrilateral

ABCD

with circumcenter

O

. Let

E

be the intersection of

AD

and

BC

, while

F

be the intersection of

AC

and

BD

. A circle

w

are tangent to

BD

and

AC

such that

F

is the orthocenter of

\triangle QEP

where

PQ

is a diameter of

w

. Prove that

EO

passes through the center of

w

.

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