MathDB

circumcenter of OIH lies on line DE if OI// BC, incenter, orthocenter

Source: 2021 Ukraine NMO 10.4 11.3

April 2, 2021

geometryCircumcenter

Problem Statement

Let

O, I, H

be the circumcenter, the incenter, and the orthocenter of

\triangle ABC

. The lines

AI

and

AH

intersect the circumcircle of

\triangle ABC

for the second time at

D

and

E

, respectively. Prove that if

OI \parallel BC

, then the circumcenter of

\triangle OIH

lies on

DE

.
(Fedir Yudin)