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ST bisects BC, <ASO = <ACO, <ATO =< ABO

Source: Switzerland - Swiss MO 2013 p7

July 16, 2020
geometrybisects segmentequal angles

Problem Statement

Let OO be the center of the circle of the triangle ABCABC with AB≠ACAB \ne AC. Furthermore, let SS and TT be points on the rays ABAB and ACAC, such that ∠ASO=∠ACO\angle ASO = \angle ACO and ∠ATO=∠ABO\angle ATO = \angle ABO. Show that STST bisects the segment BCBC.
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