Circle and a middle

[ins-]

PA and PB are tangents to the circle k(O). D is the intersection point of k and the perpendicular BC to PA. OD intersects the segment PA at the point E. F is the intersection point of k and BE. Line through F and D intersects the segment EA at the point Q. Prove that AQ=EQ.

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[ins-]

The problem is easy. Do you want a hint?

[gris]

[ins-]

<EFD=<DAB=1/2<BOD=90-<CDE=<DEC <=> QE^2=QD.QF=AQ^2

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