<Cir-2025-786>, hint

Let <AO'B=2x, <BAD=y then <CBD=x+y

Since AO'DB  are conclic , (S'''), <O'AC+<O'DC=180---><O'AC+<O'DA+<ADB+<BDC=180

90-x+(90-x-y)+x +<BDC=180 Thus <BDC=x+y.

Hence <DBC=<BDC, CB=CD

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