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a, Xét \(\Delta AKB\) có: \(\widehat{AKB}\) là góc nội tiếp chắn nửa đường tròn (chắn cung AB)

=> \(\widehat{AKB}=90^o\) hay \(\widehat{AKE}=90^o\)

b, Ta có: \(AB\perp MN\) mà AB là đường kính

=> EM = EN (liên hệ giữa đường kính và dây cung)

Dễ chứng minh được \(\Delta BMH=\Delta BNH\left(c.c.c\right)\)

=> BM = BN (2 cạnh tương ứng) => \(\stackrel\frown{BM}=\stackrel\frown{BN}\)

Xét \(\Delta BEN\) và \(\Delta BNK\) có:

\(\widehat{B}\) chung

\(\widehat{BNE}=\widehat{BKN}\) (2 góc nội tiếp cùng chắn 2 cung bằng nhau)

=> \(\Delta BEN\sim\Delta BNK\left(g.g\right)\)

=> \(\frac{BE}{BN}=\frac{BN}{BK}\Rightarrow BE.BK=BN^2\left(đpcm\right)\)

c, KE = KC (gt) => \(\Delta KEC\) vuông cân tại K => \(\widehat{KCE}=45^o\)

Xét tứ giác KHBC có: \(\widehat{H}=\widehat{K}=90^o\)

Mà 2 góc này cùng nhìn cạnh BC

=> KHBC là tứ giác nội tiếp

=> \(\widehat{KBH}=\widehat{KCH}=45^o\) (góc nội tiếp cùng chắn cung KH)

Vì OB = OK (=R) => \(\Delta OBK\) cân tại O

=> \(\widehat{BOK}=180^o-2\widehat{OBK}=90^o\)

=> \(OK\perp OB\) mà \(MN\perp OB\left(gt\right)\)

=> MN // OK

Kẻ thêm đường kính KP của đường kính (O) => KP // MN ; KP = 2R

Xét (O) có: KP và MN là 2 dây cung song song

=> \(\stackrel\frown{KN}=\stackrel\frown{MP}\Rightarrow KN=MP\)

Xét \(\Delta KMP\) có: \(\widehat{KMP}=90^o\) (góc nội tiếp chắn nửa đường tròn)

=> \(\Delta KMP\) vuông tại M

=> \(KM^2+MP^2=KP^2\)

=> \(KM^2+KN^2=KP^2=\left(2R\right)^2=4R^2\) (đpcm)

1. We can't walk there. It's very far.

=> It's too far for us to walk there.

2. Let's play the volleyball tomorrow afternoon.

=> Why don't we play the volleyball tomorrow afternoon.

3. My aunt 's baby will be born in September.

=> My aunt is going to give her baby a birth in September.

4. I intend to visit Mui Ne this summer.

=> I'm going to visit Mui Ne this summer.

Dùng từ gợi ý viết lại câu

1. . Mr. and Mrs. Lam travel to Ha Noi by plane. (FLY)

=> Mr. and Mrs. Lam fly to Ha Noi.

2.

I'd like five hundred gram of fish. (KILO)

=> I'd like half a kilo of fish.

Ex1: 1.we can't walk there.It's very far.

=>It's too far for us walk there.

2.Let's play the volleyball tomorrow afternoon.

=> Why don't we play the volleyball tomorrow afternoon.

3.My aunt's baby will be born in September

=> my aunt is going to give a birth in September.

4.I intend to visit Mui Ne this summer.

=>I'm going to visit Mui Ne this summer.

Ex 2:

1.M.r and Mrs Lam fly to Ha Noi.

2.I'd like half a kilo of fish.

Viết lại các câu sao cho nghĩa ko đổi:

1. My aunt's baby will be born in September.

=> My aunt is going to give birth to her baby in September.

2. Warm waether is good for my health.

=> I like warm weather because it is goof for my health.

3.Mr.Pike's nationality is Australia.

=> Mr.Pike is Australia.

4. We finish classes at ten to twelve.

=>We finish classes at fifty past elevn

viết lại các câu sau sao cho nghĩa ko đổi:

1,my aunt's baby will be born in september

->my aunt is going to give birth to her baby in September.

2,Warm weather is good for my health

-> I like warm weather because it is good for my health.

3,Mr.Pike's nationality is Australian

->Mr.Pike comes from Australia.

4,we finish classes at ten to twelve (viết lại câu với từ ''past'')

->We finish classes at fìfty past eleven.

Độ lớn của cường độ điện trường tại M:

\(E=E_1+E_2\) (2 điện tích cùng dấu) \(=4\cdot10^4+9\cdot10^4=13\cdot10^4\left(V/m\right)\)

Viết lại câu sao cho nghĩa không thay đổi

He goes to work t seven fifteen

--> He goes to work at a....quater past seven.......

#maymay#

1. ........she have a good time with her grandparent last time?

A. Was B. Did C. Does D. Will

2. Hung ran .......fast that he broke the world record

A. So B. Too C. Much D. Such

3. She often ........swimming with her friends in summer

A. Go B. Goes C. Went D. Gone

4. Hoa wishes she .....the exam with high score

A. Passes B.pass C. Passed D. Will pass

5. What was your brother doing when Jim........at 5 p.m yesterday?

A. Come B. Had come C. Came D. Would come

6. It's very kind ......you to help me

A. On B. Of C. In D. For

7.there is not .........for us to live in her house. It's only 40 square meters.

A. Room enough B. Enough room

C. Big enough D. Enough large

8. My parents....to Ha Noi 5 years ago

A. Move B. Moves C. Moving D.Moved

9. I wish i ......pass the mid- term test today

A. Will B. Could C. Can D. May

10. This school needs ......before the beginning of a new semester

A. To repaint B. To be repainting

C. Repainting D. Repainted

11. The boy ......next to me is my cousin

A. Sits B. Sit C. Sat D. Sitting

12. If only i .......soon, i wouldn't miss the train

A. Arrived B. Arrive C. Arriving

D. Arrives

13. You should do your homework.........

A. By yourself B. By your

C. Your own D. Myself

b/ \(\frac{1}{\sqrt{5}+2}-\sqrt{9+4\sqrt{5}}\)

\(=\frac{1}{\sqrt{5}+2}-\sqrt{\left(\sqrt{5}+2\right)^2}\)

\(=\frac{1}{\sqrt{5}+2}-\left|\sqrt{5}+2\right|\)

\(=\frac{\sqrt{5}-2}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}-\sqrt{5}-2\)

\(=\sqrt{5}-2-\sqrt{5}-2\)

\(=-4\)

Vậy..

a/ \(\frac{1}{2+\sqrt{3}}-\frac{1}{2-\sqrt{3}}+5\sqrt{3}\)

\(=\frac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}-\frac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}+5\sqrt{3}\)

\(=\frac{2-\sqrt{3}}{4-3}-\frac{2+\sqrt{3}}{4-3}+5\sqrt{3}\)

\(=2-\sqrt{3}-2-\sqrt{3}+5\sqrt{3}\)

\(=3\sqrt{3}\)

Vậy..

1.When I_____, the town hall was already full of teenagers

A.turned up B.turned off C.turned on

2.That’s enough for today-let’s_______in tomorrow

A.go up. B.go on with.(tiếp tục) C.go on

3.He’d like to have more time to_______everything before he makes a decision

A.think over. B.get over. C.take over

4.Remember to________your shoes when you enter a Japanese house

A.take over. B.take care. C.take off

5.It’s not easy to_______smoking.My unele has tried to do is lost of time without success

A.cheer up. B.give up. C.sign up

1.what .........have........Thao just(do)..................done..........?-

she (write)............has written................a letter

2.how long ......have........you(play)...............played..............guitar?-

I (play)..........have played.............it for 2 hours

3.he (not have)..........hasn't had.................cigarettes for week

4.i (not see).............haven't seen................him for month.

5.they(be)............have been..................famous in my country for years .

6.we(live)................have lived..............in this flat since we got married

7.i(know)............have known................that for a long time

8.she (drive)............has drived.............the same car since1999

9.i (play)................have played...............tennis since last month

10.he(not eat).................hasn't eaten............anything for twenty four hours

the present perfect tense

1.what ........has.........Thao just(do)........done....................?-she(write)........has written....................a letter

2.how long ......have........you(play)...............played..............guitar?-i(play).........have played...................it for 2 hours

3.he (not have)............hasn't had...............cigarettes for week

4.i (not see)..............haven't seen...............him for month.

5.they(be)...................have been...........famous in my country for years .

6.we(live)..............have lived................in this flat since we got married

7.i(know).............have known...............that for a long time

8.she (drive)...............has driven..........the same car since1999

9.i (play)..................have played.............tennis since last month

10.he(not eat)..............hasn't eaten...............anything for twenty four hours