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position of orthocenter of OXY does not depend on the choice of P on circle

Source: Tournament of Towns, Junior O-Level , Fall 2019 p2

April 19, 2020

geometryFixed pointfixedorthocentercircle

Problem Statement

Let

\omega

be a circle with the center

O

and

A

and

C

be two different points on

\omega

. For any third point

P

of the circle let

X

and

Y

be the midpoints of the segments

AP

and

CP

. Finally, let

H

be the orthocenter (the point of intersection of the altitudes) of the triangle

OXY

. Prove that the position of the point H does not depend on the choice of

P

.
(Artemiy Sokolov)