1.如圖,點(diǎn)C是射線BM上的動(dòng)點(diǎn),四邊形ABCD是矩形,對(duì)角線AC,BD交于點(diǎn)O,∠DAC的平分線交邊DC于點(diǎn)P,交射線BM于點(diǎn)F,點(diǎn)E在線段PF上(不與點(diǎn)P重合),連接EC,若2∠ECF+∠OBC=180°.
(1)證明AE=EF;
(2)點(diǎn)Q在線段EF上,連接DQ,CQ,DE,當(dāng)∠AQC=∠DAE+∠DEA時(shí),是否存在CP=DQ的情形?請(qǐng)說(shuō)明理由.