如图，$△ABC$是⊙o的内接三角形，AC=BC，D为 ⊙o中弧AB上一点，延长DA至点E，使CE=CD．

（1）求证：AE=BD；
（2）若$AC\perp BC$，求证：AD+BD=$\sqrt{2}$CD．

完形填空

    Do you like going to the movies? Most of the1 in high schools like movies very much.  Last Sunday I went to a school and asked some students2their favorite movies.3of their answers were really interesting. Here are their likes and4:

    Jim, a 5 boy, likes watching thrillers because they are scary6exciting. His classmate, Kate, can't stand documentaries. She told me they were7 parents. But she really likes comedies because they are funny. Jack is a big boy. He said he8mind documentaries. But he doesn't like comedies9they are boring! And the coolest movies are action movies. Everyone 10 them very much!

已知函数f（x）=sinωx+acosωx（a＞0，ω＞0）的图象关于直线x=$\frac{\mathrm{\pi }}{6}$对称，点（$\frac{2\mathrm{\pi }}{3}$,0）是函数图象的一个对称中心，则a+ω的最小值是____