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2019 MMATHS Tiebreaker p2 - tangential ABCD with 2 right angles

Source:

October 7, 2023
MMATHSgeometry

Problem Statement

In the trapezoid ABCDABCD, both B\angle B and C\angle C are right angles, and all four sides of the trapezoid are tangent to the same circle. If AB=x\overline{AB} = x and CD=y\overline{CD} = y, find the area of ABCDABCD (with proof).