Cho (O;R) và điểm A ngoài (O) , OA=R√2, vẽ (I) đường kính OA cắt (O) tại B và C

a) Chứng minh AB, AC là tiếp tuyến của (O).

b) Tứ giác ABOC ?

c) Đường thẳng OA cắt (O) tại D và E

Chứng minh: AB\(^{ }\)^2=AD.AE

d) Đường thẳng AMN lầ 1 cát tuyến bất kỳ của (O). Tìm tập hợp các trung điểm K của MN.

Cho O là trung điểm. Vẽ Ax, By vuông góc với AB (cùng 1 nửa mặt phẳng bờ AB). C ∈ Ax, D ∈ By sao cho ∠COD=90°, DH⊥CD.

a) Chứng minh: H thuộc đường tròn tâm O bán kính AB.

b) Xác định vị trí của đường thẳng CD và đường tròn tâm O.

Supply the correct verb forms.

1. We would rather (stay) home tonight.

2. Mr Jones would rather (stay) at home last night.

3. We would rather (drink) coffee than tea.

4. The photographer would rather that we (stand) closer together than we are standing.

5. Carmen would rather (cook) for the entire family.

6. She would rather you (not arrive) last night.

7. John would rather you (sleep) than worked last night.

8. George would rather Jane (be) here tomorrow.

9. I would rather my sister (not, fail) the driving test yesterday.

10. I would rather that they (invite) her to their party last Sunday.

11. Henry talks to his dog as if it (understand) him.

12. It's time we all (go) now.

13. I'd rather you (go) now.

14. It's high time you (get) the tea ready.

15. He acts as if he (know) English perfectly.

16. I'd rather you (play) me now.

17. It's high time you (have) a haircut.

18. He was wet as if he (swim) for hours.

19. She acted as if she (meet) him before.

20. Jack spent his money as if he (win) a lottery.

Make clauses of concession with WHATEVER.

1. No matter what happens, don't forget to write to me.

2. She will refuse to consider our proposal even if we made any kinds of effort to persuade her.

3. No matter what kinds of exercises he had taken, he was still putting on weight.

4. No matter what sorts of difficulties you may encounter, you should keep your promise.

5. No matter what he says, nobody believes him.

6. You should review all your lessons before taking your exam although you have any kinds of difficulties.

7. Although he had taken any kinds of exercises, he got fatter and fatter.

8. You should always study hard although you encounter difficulties.

9. Although others may say anything, she is certainly right.

10. Although he chose any job, his parents were pleased with him.

Combine each pair of sentences below, using the conjunction given in parentheses.

1. He is very rich. He isn't happy. (Although)

2. He is very rich. He isn't happy. (No matter)

3. She can't answer my question. She is very intelligent. (Although)

4. She can't answer my question. She is very intelligent. (No matter)

5. He does anything. He is always careful. (Whatever)

6. He does anything. He always tries his best. (No matter)

7. She says anything. I don't believe her. (Whatever)

8. She says anything. I don't believe her. (No matter)

9. He tried. He was not successful. (No matter)

10. He tried. He was not successful. (Although)

11. His life is hard. He is determined to study well. (Although)

12. His life is hard. He is determined to study well. (No matter)

13. He was wise and experienced. He was taken in. (Thought)

14. He got good jobs. He was not satisfied. (No matter)

15. He got good jobs. He was not satisfied. (Even though)

16. You do any job. You should do it devotedly. (Whatever)

17. He lived anywhere. He always thought of his homeland. (No matter)

18. It was cold. He didn't wear warm clothes. (No matter).

19. He often tells lies. Many people believe him. (Although)

20. You return at any time. She waits for you. (No matter)

Change clauses of reason to phrases.

1. Mary didn't go to school yesterday because she was sick.

2. She went to bed early because she felt tired.

3. Ann didn't go to the circus with Betty because she had a bad cold.

4. John succeeded in his exam because he worked hard and methodically.

5. Margaret stayed home because her mother was sick.

6. I like him because his father is kind to me.

7. I can't eat these fruits because they are green.

8. I couldn't do the test because it was difficult.

9. I couldn't read the letter because it was dark.

10. He came late because it rained heavily.

11. I can't study because it is noisy.

12. The train came late because it was foggy.

13. All the teachers love him because his conduct is good.

14. The train was late because the fog was thick.

15. We stopped our car because the traffic lights turned red.

16. The plane couldn't take off because the weather was bad.

17. Rice plants grow well because the climate is warm and damp.

18. He couldn't drive fast because the street was crowded and narrow.

19. I can't sleep because the weather is hot.

20. He left school because his life was hard.

Rewrite these sentences, using BECAUSE.

1. It's raining, so we stay at home.

2. Most people hear jogging is a good exercise, so they begin to jog.

3. The climate in the country is healthy, so people like to live there.

4. A computer can be used for various purposes, so it becomes very popular nowadays.

5. Tommorow is a public holiday, so all the shops will be shut.

Make questions with WHY.

1. I left school because of my hard life at the time.

2. The train was late because the fog was thick.

3. They'll leave early because the distance is very long.

4. She likes him because he is kind.

5. The pupil understood that mathematical problem very well because he explained it clearly.