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Problem 2 — Angle from Triangle Lines Must Be Right

Source: 46th Austrian Mathematical Olympiad National Competition Part 1 Problem 2

July 14, 2018
Austriageometry

Problem Statement

Let ABCABC be an acute-angled triangle with AC<ABAC < AB and circumradius RR. Furthermore, let DD be the foot ofthe altitude from AA on BCBC and let TT denote the point on the line ADAD such that AT=2RAT = 2R holds with DD lying between AA and TT. Finally, let SS denote the mid-point of the arc BCBC on the circumcircle that does not include AA.
Prove: ∠AST=90∘\angle AST = 90^\circ.
(Karl Czakler)
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