如圖,已知在Rt△ABC中,AB=BC,∠ABC=90°,BO⊥AC于點(diǎn)O,點(diǎn)P、D分別在AO和BC上,PB=PD,DE⊥AC于點(diǎn)E.
(1)若PB平分∠ABO,求證:AP=CD;
(2)若點(diǎn)P是一個(gè)動(dòng)點(diǎn),點(diǎn)P運(yùn)動(dòng)到OC的中點(diǎn)P′時(shí),滿足題中條件的點(diǎn)D也隨之在直線BC上運(yùn)動(dòng)到點(diǎn)D′,請(qǐng)直接寫出CD′與AP′的數(shù)量關(guān)系.(不必寫解答過程)