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A convex quadrilateral

Source:

May 12, 2006
geometryperimeterfloor functiontrigonometrycircumcircletrig identitiesLaw of Cosines

Problem Statement

In convex quadrilateral ABCDABCD, ∠A≅∠C\angle A \cong \angle C, AB=CD=180AB = CD = 180, and AD≠BCAD \neq BC. The perimeter of ABCDABCD is 640. Find ⌊1000cos⁡A⌋\lfloor 1000 \cos A \rfloor. (The notation ⌊x⌋\lfloor x \rfloor means the greatest integer that is less than or equal to xx.)
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