发现：

（1）若干平面上三点能够确定一个圆，那么这三点所满足的条件．

（2）我们判断四个点A，B，C，D（任意其中个三点不共线）是否在同一圆上时，一般地，先作过A，B，C三点的圆，然后判断点D是否在这个圆上，如果在，则这四个点共圆，如果不在，则不存在同时过这四个点的圆．

思考：

（1）如图1，∠ACB=∠ADB=90°，那么点A，B，C，D四点在不在同一个圆上；

（2）如图2，如果∠ACB=∠ADB=a（a≠90°），（点C，D在AB的同侧），那么点D还在经过A，B，C三点的圆上吗？芳芳已经证明了点D不在圆内（如图所示），只要能够证明点D也不再圆外，就可以判断点D一定在圆上了，请你完成证明过程．

芳芳的证明过程：

如图3，过A，B，C三点作圆，圆心为O．假设点D在⊙O内，设AD的延长线交⊙O于点P，连接BP．易得∠APB=∠ACB．又由∠ADB是△BPD的外交，得到∠ADB＞∠APB，因此∠ADB＞∠ACB，这个结论与条件中的∠ACB=∠ADB矛盾，所以点D不在圆内．

应用：

如图4，在四边形ABCD中，连接AC，BD，∠CAD=∠CBD=90°，点P在CA的延长线上，连接DP．若∠ADP=∠ABD．求证：DP为Rt△ACD的外接圆的切线．

已知tan$\theta$=$\frac{4}{3}$，则$\frac{\sin \theta +\cos \theta }{\sin \theta -\cos \theta }$的值为（　　）

阅读与回答问题。

    New rules and behavior standards for middle school students came out in March. Middle schools are going to use a new way to decide who the top students are. The best students won't only have high marks. They will also be kids who don't dye(染) their hair. The following are some of the new rules.

    Tell the truth. Have you ever copied someone else's work on an exam? Don't do it again! That's not something an honest student should do. If you have played computer games for two hours in your room, don't tell your parents you have done homework.

    Do more at school. Good students love animals and care for other people. April is Bird-loving month in China. Is your school doing anything to celebrate? You should join! In that way, you can learn more about animals and how to protect them. When more people work together, it makes it more fun for everyone. Have you ever quarreled with your teammates when your basketball team lost? Only working together can make your team stronger. Be friendly to the people you are with. Try to think of others, not only yourself.

    Be open to new ideas. Have you ever thought that people could live on the moon? Maybe you'll discover Earth Ⅱ some day. Don't look down on new ideas. Everyone's ideas are important. You should welcome them, because new ideas make life better for everyone.

    Protect yourself. Has someone ever taken money from one of your classmates? Don't let it happen to you. If you have to go home late, you should let your parents know.

    Use the Internet carefully. The Internet can be very useful for your studies. But some things on the Internet aren't for kids, so try to look at web pages that are good for you. You can use the web for fun or homework. Can't you find any good websites for children? Here are some: Http:// kids.eastday.com, Http://www. chinakids. net. com, http ://www. cycnet.com.