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Cyclic quad

Source: The South African Mathematical Olympiad Third Round 2023 P2

July 30, 2023
geometrycyclic quadrilateral

Problem Statement

ABCDABCD is a cyclic quadrilateral with ∠BAD=90∘\angle BAD=90^\circ and ∠ABC>90∘\angle ABC>90^\circ. ABAB is extended to a point EE such that ∠AEC=90∘\angle AEC=90^\circ.If AB=7,BE=9,AB=7,BE=9, and EC=12EC=12,calculate ADAD.
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