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Kosovo Mathematical Olympiad 2016 TST , Problem 5

Source:

January 9, 2017
geometry

Problem Statement

Let be ABCABC an acute triangle with ∣AB∣>∣AC∣|AB|>|AC| . Let be DD point in side ABAB such that ∠ACD=∠CBD\angle ACD=\angle CBD . Let be EE the midpoint of segment BDBD and SS let be the circumcenter of triangle BCDBCD . Show that points A,E,SA,E,S and CC lie on a circle .
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