28.如圖,在矩形ABCD中,AB=4,AD=2,動(dòng)點(diǎn)P從點(diǎn)A開(kāi)始以每秒2個(gè)單位長(zhǎng)度沿AB向終點(diǎn)B運(yùn)動(dòng),同時(shí),動(dòng)點(diǎn)Q從點(diǎn)C開(kāi)始沿C-D-A以每秒3個(gè)單位長(zhǎng)度向終點(diǎn)A運(yùn)動(dòng),它們同時(shí)到達(dá)終點(diǎn).連接PQ交AC于點(diǎn)E.過(guò)點(diǎn)E作EF⊥PQ,交直線(xiàn)CD于點(diǎn)F.
(1)當(dāng)點(diǎn)Q在線(xiàn)段CD上時(shí),求證:
;
(2)當(dāng)DQ=1時(shí),求△APE的面積;
(3)在P,Q的運(yùn)動(dòng)過(guò)程中,是否存在某一位置,使得以點(diǎn)E,F(xiàn),Q為頂點(diǎn)的三角形與△ABC相似?若存在,求BP的長(zhǎng);若不存在,請(qǐng)說(shuō)明理由.