题目

（本题满分9分）如图所示，△ABC内接于⊙O，AB是⊙O的直径，点D在⊙O 上，过点C的切线交AD的延长线于点E，且AE⊥CE，连接CD．（1）求证：DC=BC；   （2）若AB=5，AC=4，求tan∠DCE的值．  答案：（1）证明：连接OC················································································· 1分∵OA＝OC∴∠OAC＝∠OCA ∵CE是⊙O的切线∴∠OCE＝90° ·············································· 2分∵AE⊥CE∴∠AEC＝∠OCE＝90°∴OC∥AE11．下列各组离子，能在溶液中大量共存的是（　　）A．Fe2+．Na+．NO3-．H+B．NH4+．Fe3+．SO42-．SCN-C．Ca2+．K+．CO32-．OH-D．SO42-．Cl-．Cu2+．Mg2+