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SMT 2018 Geometry #3 area

Source:

August 8, 2023
geometry

Problem Statement

Let ABCABC be a triangle and DD be a point such that AA and DD are on opposite sides of BCBC. Give that ∠ACD=75o\angle ACD = 75^o, AC=2AC = 2, BD=6BD =\sqrt6, and ADAD is an angle bisector of both △ABC\vartriangle ABC and △BCD\vartriangle BCD, find the area of quadrilateral ABDCABDC.
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