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prove two lines are perpendicular

Source: Mathematics Regional Olympiad of Mexico Southeast 2019 P2

October 23, 2021
geometry

Problem Statement

Let ABCDABCD a convex quadrilateral. Suppose that the circumference with center BB and radius BCBC is tangent to ADAD in FF and the circumference with center AA and radius ADAD is tangent to BCBC in EE. Prove that DEDE and CFCF are perpendicular.
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