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Points A, E, S and C lie on the same circle [Slovenia 2010]

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November 16, 2010
geometrycircumcirclegeometry proposed

Problem Statement

Let ABCABC be an acute triangle with ∣AB∣>∣AC∣.|AB| > |AC|. Let DD be a point on the side ABAB, such that the angles ∠ACD\angle ACD and ∠CBD\angle CBD are equal. Let EE denote the midpoint of BD,BD, and let SS be the circumcenter of the triangle BCD.BCD. Prove that the points A,E,SA, E, S and CC lie on the same circle.
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