Advanced Geometric Problem & Solution (Twice a week update) Now 4604 problems posted.
<Qua-2025-768>, hint
Let <FAE=<FAD=X and AB=a, AD=b
DF+BE=AE <--> btanX+atan(90-2X)=a/(cos(90-2X))
b (sinX/cosX)+a(cos2X/sin2X)=a/sin2X. sin2X=2sinX cosX, cos2X=1-2sin^2(X)
Finally (b-a) tanX=0. Hence a=b.
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