地理分界线对我们了解地理现象和地理事物分布轨律具有十分重要的作用，读“我国一些主要地理界线图”，回答下题．

如图，已知直线PA交⊙O于A、B两点，AE是⊙O的直径,点C为⊙O上一点，且AC平分∠PAE，过C作CD⊥PA，垂足为D.

（1）求证：CD为⊙O的切线；
（2）若CD=2AD，⊙O的直径为10，求线段AB的长.

    About 70，000，000 Americans are trying to lose weight．This is almost one out of every three people in the United States．Some people eat 1food and they hardly have any fats or sweets. Others do running exercise with machines，take medicines，or even have operations2you can see losing weight is 3 work，and it will also cost a lot of money．But 4do so many people in the United States want to lose weight?
    Many people in the United States worry about their look of the body．For many people，looking nice also means to be 5．Other people worry about their health as many doctors 6 overweight is not good．
    Most people want to find a faster and 7 way to take off fat，and books of this kind are very popular．These books tell people how to lose weight．Each year a lot of new books like these are 8．Each one says it can easily help people take fat away．
    Losing weight can be expensive．Some overweight people go to health centers，like La Costa in California．Men and women9several hundred dollars a day at these health centers．People live there for one week or two，taking exercise，eating different foods．Meals there may be just a little．All this works for losing weight．104 days on the program，one woman called Mrs. Warren lost 5 pounds(2.27kg)．At 400 dollars a day, she spent 320dollars to lose each pound．But she said she was still glad to do so．
    Health centers，books，medicines，operations，running and exercise machines all get a lot of money．So in the United States，losing weight may mean losing money too.

Betty enjoys playing ______ piano while her brother lovers playing ______ basketball.