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Circumcenter of $AHO$ and Euler Line

Source: Turkey National Mathematical Olympiad 2022 P5

December 23, 2022

geometry

Problem Statement

In triangle

ABC

90^{o}> \angle A> \angle B> \angle C

. Let the circumcenter and orthocenter of the triangle be

O

and

H

OH

intersects

BC

T

and the circumcenter of

(AHO)

X

. Prove that the reflection of

H

over

XT

lies on the circumcircle of triangle

ABC