MathDB
TH bisects BC, circumcircle of acute related (2010 Kyiv City MO 9.4 )

Source:

July 13, 2020
geometrycircumcirclebisects segment

Problem Statement

In an acute-angled triangle ABCABC, the point OO is the center of the circumcircle, CHCH is the height of the triangle, and the point TT is the foot of the perpendicular dropped from the vertex CC on the line AOAO. Prove that the line THTH passes through the midpoint of the side BCBC .