题干

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.

 

上一题 下一题 0.0难度 选择题 更新时间:2016-09-27 01:41:00

答案(点此获取答案解析)

解:发现:(1)若平面上三点能够确定一个圆,那么这三点所满足的条件是三点不在同一条直线上,故答案为:三点不在同一条直线上;思考:(1)∠ACB=∠ADB=90°,那么点A,B,C,D四点在同一个圆上,故答案为:在;(2)如图①,假设点D在⊙O外,设AD交⊙O于点E,连接BE,易得∠AEB=∠ACB,又由∠AEB是△BED的外角,∴∠AEB>∠D,∵∠ACB=∠AEB,∴∠ACB>∠ADB,这个结论与条件中的∠ACB=∠ADB矛盾,∴点D不在圆外,∴D一定在圆上;应用:∵∠CAD=∠CBD=90°,∴A,B

同类题1

阅读理解

Protect Children from Cyber-bullying

    When you think about bullying, you might think of a child being bullied by another in the schoolyard. As more young people have access to computers and cell phones, traditional bullying has gone digital, which has not yet gained awareness in Chinese parents.

    Cyber-bullying, first invented by Canadian educator Bill Belsey, is the use of the Internet and related technologies to harm other people, in an intentional, repeated, and unfriendly manner. It involves threatening text messages, the spread of online rumors on social networking sites, and intentionally keeping someone out of an online group. Cyber-bullying is at an all-time high in the US. According to a study from the US Department of Justice, more than 43% of teenagers report being victims(受害者)of cyber-bullying.

    Compared to face-to-face bullying, cyber-bullying is considered to have a worse emotional effect on the victims, and kids could feel more desperate and depressed. Severe, long-term or frequent cyber-bullying can leave victims at greater risk for anxiety, depression, and other disorders. Research says that cyber-bullying victims were almost twice as likely to have attempted suicide compared to youths who had not experienced it.

    In traditional schoolyard bullying, at least home is a safe place for the victims. But cyber-bullying is endless---it could happen anytime. Moreover, in the digital world, bullying is much easier, as a bully can pick on people with a much lower risk of being caught.

    Actually, cyber-bullying has become a worldwide issue. In the US, as several teens committed suicide because of cyber-bullying, some schools set rules to punish cyberbullies. Laws to punish cyber-bullying have been introduced in some states. In China, cyber-bullying is still considered by many parents and educators as a problem that involves physical contact. However, as cell phones and laptops are becoming common equipment for teenagers, social interactions have increasingly moved from personal contact to virtual contact. Cyber-bullying is spreading faster than expected.

    For schools and parents, safety rules should be set in the virtual world for kids, such as telling them not to let out anything to a stranger. Active steps should be taken to make the public aware of the seriousness of this problem, because it would be too late to take measures after tragedy strikes.