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A circle containing nine-point cener

Source: 2019 Belarus Team Selection Test 2.2

September 2, 2019
geometrycircumcircleperpendicular bisectorBelarusgeometry solvedNine point centerEuler Line

Problem Statement

Let OO be the circumcenter and HH be the orthocenter of an acute-angled triangle ABCABC. Point TT is the midpoint of the segment AOAO. The perpendicular bisector of AOAO intersects the line BCBC at point SS. Prove that the circumcircle of the triangle ASTAST bisects the segment OHOH.
(M. Berindeanu, RMC 2018 book)
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