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Euclidean 2Dhard
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Find the area of a quadrilateral ABCDABCDABCD inscribed in a circle, given AB=9,BC=12,CD=8,AB=9, BC=12, CD=8,AB=9,BC=12,CD=8, and AD=6AD=6AD=6, such that ∠ABC+∠ADC=180∘\angle ABC + \angle ADC = 180^{\circ}∠ABC+∠ADC=180∘.