<Qua-2025-753>, hint

Since OE is bisector of  <DOA, DE/EA=OD/OA. Let AD=d, <OAD=x DE/DA= d sinx/d cosx

CD=d tan x, AB=d cot x, EP/CD=AE/AD =QF/CD  ---> EP=QF

EF=EQ+QF--EQ=AB X DE/AD  QF=PE=CD X AE/AD

EQ=AB X DE/AD  <-EQ=AD cotx  X DE/AD= d cotx X d sinx/(dsinx+cosx) 

=d cosx/(sinxx+cosx). Similarly FQ=EP= CD X AE/AD=d sinx /(sinx+cosx)

Hence EF=EQ+QF= d(cosx+sinx)/(sinx+cosx)=d=AD