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concyclic wanted, incenter, perp. bisector, angle bisectors

Source: 2020 Austrian Regional Competition For Advanced Students p3

November 22, 2020
geometryConcyclicincenter

Problem Statement

Let a triangle ABCABC be given with AB<ACAB <AC. Let the inscribed center of the triangle be II. The perpendicular bisector of side BCBC intersects the angle bisector of BACBAC at point SS and the angle bisector of CBACBA at point TT. Prove that the points C,I,SC, I, S and TT lie on a circle.
(Karl Czakler)
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