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Problem 4 -- Circling Parallel Lines

Source: 47th Austrian Mathematical Olympiad Regional Competition Problem 4

July 27, 2018
geometrycircumcircleAustria

Problem Statement

Let ABCABC be a triangle with AC>ABAC > AB and circumcenter OO. The tangents to the circumcircle at AA and BB intersect at TT. The perpendicular bisector of the side BCBC intersects side ACAC at SS.
(a) Prove that the points AA, BB, OO, SS, and TT lie on a common circle. (b) Prove that the line STST is parallel to the side BCBC.
(Karl Czakler)
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