Cho đường tròn (O;R) và điểm A nằm ngoài đường tròn. Từ A vẽ các tiếp tuyến AB, AC của (O;R), (BC là các tiếp điểm).

1) Chứng minh rằng bốn điểm A,B,O,C cùng thuộc một đường tròn;

2) Lấy điểm I trên đường tròn (O;R) sao cho tia OI nằm giữa hai tia OA và OB. Qua I vẽ đường thẳng tiếp xúc với đường tròn (O;R) cắt AB,AC lần lượt tại M và N. Chứng minh MB+NC=MN;

3) Qua O vẽ đường thẳng vuông góc với OA cắt AB,AC lần lượt tại P và Q. Chứng minh rằng PM.QN=\(\frac{PQ^2}{4}\)

                    I.The following passage contains ten errors. Find and correct them.

Things started to go wrongly as soon as we got to the hotel. We were all completely exhaustingafter our long journey and looking forward to a shower and a rest. However, we found that our room was not ready, which was very annoyed, although the manager was extremely apologising. While we were waiting, we asked about the excursions to places of an interest which we have readabout in the brochure. Imagine how we felt when we were told they had all been cancelled! Apparently, the person responsible of organizing them had left suddenly and had not been replaced. Then Sally saw a notice pinning to the door of the restaurant, said it was closed for redecoration, and Peter discovered that the swimming pool was empty. When we eventually got to our room we were horrified to find that it was at the back of the hotel, and we had a view of a car park, thatseemed to be used as a rubbish dump. We seriously began to wonder whether or not to stay.

                    II. Read the text below, using the word given in brackets to form a word that fits in the space.

Congratulations to all involved with the school (__1__ produce) of The Woman Next Door. The (__2__ advertise) was carried out by the Art Department, and the posters were very (__3__ imagine). We certainly have some very (__4__ art) students in our school! Many people helped with building and painting the (__5__ scene) and the play was written by the English Department, who managed to create an (__6__ amuse) story, with excellent songs. The music was written by Sue Porter, who also (__7__ company) the singers on the piano. Everyone enjoyed a thoroughly (__8__ entertain) evening, and there was a long round of (__9__ applaud) at the end. Jim Barrett gave a brilliant performance as Sergeant Moss, and Liz Aiken was a (__10__delight) Mrs. Jump. Well-done everyone!