Cho tam giác ABC có góc A 90 độ, đường cao AH. Biết \(\dfrac{AH}{AC}=\dfrac{3}{5}\)và AB=12cm

a/Tính HB,HC

b/ Gọi E,F là hình chiếu H lên AB,AC.CHứng minh \(AH^3=BC.BE.CF\)

c/ Chứng minh trung tuyến AM của tam giác ABC vuông góc với EF

d/ Giả sử diện tích tam giác ABC gấp 2 lần diện tích AEHF. CHứng minh tam giác ABC vuông cân

Rút gọn

\(B=sin\alpha-sin\alpha.cos^2\alpha\)

\(C=\left(tg46^o+cotg46^o\right)-\left(tg46^o-cotg46^o\right)^2\)

Finish each of the following sentences in such a way that it means exactly the same as the sentences printed before it

1. You must submit artcles for the magazine by June 18th

-> The final date...............................................................

2. Marthin may not be very well but he still manages tp enjoy life.

-> Martin's poor.....................................................

3. We weren't surprised by his success.

->It came............................................

4. The hurricane blew the roof off the house.

=> the house......................................................................

5. It is not certain that Jones will get the job.

-> it is open.....................................................................

6. The drama critic of the Daily News regards the new play as a major breakthrough.

-> According to................................................................................

7. Arthur said he was sorry he had hurt her feelings

-> Athur apologised................................................

8. I'm sorry now that I asked her to stay.

-> Now I wish......................................

9. He remembered, and so did she.

-> He didn't.............................................

10. When are the council going to do something about the city's traffic problem?

-> it's high time something.................................................................

Finish each of the following sentences in such a way that it means exactly the same as the sentences printed before it

1.These new machines have put an end to queuing.

->Before these..............................................

2. There was no precedent for the king's resignation.

-> Never.................................................................

3.The fisherman's life was one of great poverty.

->Throughout...........................................................

4.I didn't realise he was your brother until I saw the photograh.

-> It was only..................................................................

5. John and Mary moved to Edinburgh twenty years ago.

-> It is..........................................................

6. It was Walter Raleigh who introduced potatoes and tobacco into England.

-> The English owe......................................................................

7.One runner was too exhausted to complete the last lap of race.

-> One runner was so............................................

8. You can eat as much as you like for $5 at the new luch-bar.

-> There is no.....................................................

9. The protest has been so vociferous that the commitlee has had to reconsider.

-> there has been................................................................................

10 It was the goalkeeper who saved the match for us.

-> If it hadn't.........................................................

Finish each of the following sentences in such a way that it means exactly the same as the sentences printed before it

1. "Don't move or I'll shoot" the bank robber said to the clerk.

-> The bank robber threatened......................................................

2. "I must see the manager" he cried

-> He insisted.....................................

3. He said he was not guilty of stealing the car.

=> He denied.............................................

4. He insisted on a full apology.

->Nothing but..........................................

5. The crities were very impressed by her performance.

-> Her performance made.....................................

6. Helen can play the piano better than Elizabeth.

-> Elizabeth.........................................................

7. He said "I wish I knew the answer"

-> He said that................................

8. She is proud of being such a good cook.

-> She brides................................................

9. May I borrow your pen?

Would you..................................................

10 Oil was slowly coating the edge of the shore.

-> The adge of the shore..........................................

11 "If Brian doesn't train harder, I won't select him for the team" said the manager.

-> The manager threatened.....................................................................................

Finish each of the following sentences in such a way that it means exactly the same as the sentences printed before it

1. I had only just put the phone down when the boss rang back.

-> Hardly.........................................................

2. That rumour about the politician and the construction contract is absolutely false.

-> There is....................................................

3.He was sentences to six months in rpison for his part in the robbery.

-> He received a............................................................

4.The salesman told me that my new car would be delivered next Wednesday.

-> According.......................................................................

5. Immediately after his appointment to the post, the new aditor fell ill.

-> No sooner.................................................

6. Mrs Scott is proud of her cooking.

-> Mrs Scott prides..................................................

7. This affair does not concern you.

-> This affair is no.........................................

8. You are under no obligation to accept their offer.

-> you can please............................................

9. I am amazed by the mistakes he makes.

-> What...............................

Finish each of the following sentences in such a way that it means exactly the same as the sentences printed before it

1. His second attempt on the world record was successful.

-> He broke...............................................

2. The Prime Minister was determined to remain in office.

->The Prime Minister had no.........................................

3. Despite his ungainly air he is remarkably agile.

-> Although...............................

4. He fogot about the gun until he got home.

-> Not until.......................................

5. the truth only came out on the publication of the general's pesonal diaries.

-> Only when...........................................................

6. The house seemed to have been unoccupied for several months.

-> It looked..............................................................

7. For a teacher of her experience and ability, discripline was not a problem.

-> For such.............................................................................

8. If she hadn't insisted on kissing everyone goodbye she woulf have caught the train.

-> if it hadn't...................................................................

9. They were unable to finish their game of tennis because of a heavy shower.

-> A heavy shower......................................................

10. If you missed the programme you can't really judge.

-> Unless you..................................................................

Finish each of the following sentences in such a way that it means exactly the same as the sentences printed before it

1. The rail workers do not intend to call off their strike.

-> The rail workers have no.....................................

2. House prices have risen dramatically this year.
-> There has..............................

3. Alce and CHarles did not decide to move to a bigger house until after the birth of their second son.
-> Only when..............................................................
4. The film star wore dark glasses so that no one would recognise him.
-> The film star avoided....................................
5. No-one has challenged his aithority before.
-> This is the first time.........................................
6. If it doesn't rain soon, milions of pounds's world of crops will be lost.
-> Unless..........................................
7. "I don't love you anymore" said Eric to his girlfriends.
-> Eric told his girlfriends that.....................................
8. My father speaks very little English.
-> My father speaks hardly.........................................
9. That dress has only the slightest mark on it.
-> I can barely .....................................
10. No matter how hard I tried I couldn't open the door.
-> try......................................