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point on the altitude

Source: Bulgaria NMO 2021P2

May 16, 2021
geometry

Problem Statement

A point TT is given on the altitude through point CC in the acute triangle ABCABC with circumcenter OO, such that ∡TBA=∡ACB\measuredangle TBA=\measuredangle ACB. If the line COCO intersects side ABAB at point KK, prove that the perpendicular bisector of ABAB, the altitude through AA and the segment KTKT are concurrent.
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