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circumcircle of ADE bisects OH, circumcenter, orthocenter

Source: 2012 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p7

April 26, 2021

geometrybisects sementsUkraine Correspondence

Problem Statement

Let

O

and

H

be the center of the circumcircle and the point of intersection of the altitudes of the acute triangle

ABC

respectively,

D

be the foot of the altitude drawn to

BC

, and

E

be the midpoint of

AO

. Prove that the circumcircle of the triangle

ADE

passes through the midpoint of the segment

OH