MathDB

2012.7

Part of Ukraine Correspondence MO - geometry

Problems(1)

circumcircle of ADE bisects OH, circumcenter, orthocenter

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

4/26/2021
Let OO and HH be the center of the circumcircle and the point of intersection of the altitudes of the acute triangle ABCABC respectively, DD be the foot of the altitude drawn to BCBC, and EE be the midpoint of AOAO. Prove that the circumcircle of the triangle ADEADE passes through the midpoint of the segment OHOH.
geometrybisects sementsUkraine Correspondence