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condition for equal angles wanted, isosceles trapezoid, tangents of circumcircle

Source: 2019 Austrian Federal Competition For Advanced Students, Part 2 p2

March 5, 2020
geometrytrapezoidTangentsCyclicisoscelesequal anglescircumcircle

Problem Statement

A (convex) trapezoid ABCDABCD is good, if it is inscribed in a circle, sides ABAB and CDCD are the bases and CDCD is shorter than ABAB. For a good trapezoid ABCDABCD the following terms are defined: ∙\bullet The parallel to ADAD passing through BB intersects the extension of side CDCD at point SS. ∙\bullet The two tangents passing through SS on the circumircle of the trapezoid touch the circle at EE and FF, where EE lies on the same side of the straight line CDCD as AA. Give the simplest possible equivalent condition (expressed in side lengths and / or angles of the trapezoid) so that with a good trapezoid ABCDABCD the two angles ∠BSE\angle BSE and ∠FSC\angle FSC have the same measure.
(Walther Janous)
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