(2014?遂宁)已知:如图,⊙O的直径AB垂直于弦CD,过点C的切线与直径AB的延长线相交于点P,连结PD.(1)求证:PD是⊙O的切线.(2)求证:PD2=PB?PA.(3)若PD=4,tan∠CDB=12,求直径AB的长.