问题 填空题

圆外切等腰梯形的底角为30°,中位线的长为8,则该圆的直径长为______.

答案

根据题意画出相应的图形,过A作AM⊥BC于M点,如图所示:

∵梯形ABCD的中位线为8,

∴AD+BC=2×8=16,

即AE+ED+BG+GC=16,

又梯形为圆的外切梯形,

∴梯形各边与圆相切,

∴AE=AF,DE=DH,BF=BG,CG=CH,

∴AF+FB+DH+HC=16,即AB+CD=16,

又梯形ABCD为等腰梯形,

∴AB=CD=8,

在Rt△ABM中,∠B=30°,∠AMB=90°,AB=8,

则AM=

1
2
AB=4,即圆的直径为4.

故答案为:4

多项选择题
阅读理解

阅读理解

     It happened to me recently that I was telling someone how much I had enjoyed reading Barack

Obama's Dreams from My Father and how it had changed my views of the current US president.The

person I was talking to agreed with me that it was,in his words,"a wonderfully written book".However,he

then proceeded to talk about Mr Obama in a way that suggested he had no idea of his background at all.I

sensed that I was talking to a book liar.

     And it seems that he is not the only one.Clearly two thirds of people have lied about reading a book B

which they haven't.In the World Book Day survey,Dreams from My Father is at number 9.The survey

lists top ten books,and various authors,which people have lied about reading.As I'm not one to lie too

often,I'll admit here and now that I haven't read the entire ten books.But I am pleased to say that I have

read the book at number one,George Orwell's 1984.I think it's absolutely outstanding.

     Asked why they lied,the most common reason was to impress someone they were speaking to.This

could be difficult if the conversation became more indepth!

     The World Book Day survey also has some other interesting information in it.It shows that many people

lie about having read classical works by Jane Austen,the Bronte sisters,Charles Dickens and so on.But

when asked which authors they actually enjoy,they named J.K.Rowling,Jilly Cooper,and Stephen King

(ah,the big sellers,in other words).Fortyone percent of people asked admitted they turned to the back of

the book to read the end before finishing the story.

     So which books have you lied about reading-if any-and which is your favourite?

1. The main reason why people lie about reading is to _____.

A. make fun of the listener

B. impress the listener

C. please the listener

D. interest the listener

2. The underlined word"proceeded" in the passage probably means "_____".

A. wanted  

B. happened

C. continued  

D. stopped

3. What does the World Book Day survey show?

A. Nearly half of the people surveyed didn't read through a whole classical book.

B. People don't like Dreams from My Father and George Orwell 's 1984.

C. Few people lie about having read classical works by Jane Austen.

D. People usually enjoy reading books by Charles Dickens.

4. What is the best title for the passage?

A. Are You a Book Liar?  

B. Readers Are All Liars

C. World Book Day  

D. Dreams from My Father