<Polygon-2024-274>, hint


 Let orthogonal projections of E onto AB, CD, AC, BD be P,Q, R, S 

Since ABDE are concyclic <EAP=<EDS

 and ACDE are concyclic <EAR=<EDQ

EP=EA sinEAP, ER=EAsinEAR  and ES=EDsinEDS, EQ=sinEDQ

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