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Part of 2003 Turkey Junior National Olympiad

Problems(1)

Turkey Junior Olympiad 2003, Part II - P1

Source:

1/20/2013
Let ABCDABCD be a cyclic quadrilateral, and EE be the intersection of its diagonals. If m(ADB^)=22.5∘m(\widehat{ADB}) = 22.5^\circ, ∣BD∣=6|BD|=6, and ∣AD∣⋅∣CE∣=∣DC∣⋅∣AE∣|AD|\cdot|CE|=|DC|\cdot|AE|, find the area of the quadrilateral ABCDABCD.
geometrytrigonometryquadraticscyclic quadrilateraltrig identitiesLaw of Cosines