"Everything is established in advance, and if it is not planned, it will be abolished." It's best to draw up a study plan briefly every week, preferably from Monday to Friday night, what you need to do after your homework is completed, what to do, what to learn and what to review at each time on weekends in the morning, afternoon and evening.
Second, firmly grasp the foundation.
The focus of the exam is still basic knowledge. The analysis of all test papers in junior high school is basically basic knowledge, and the proportion of difficult questions is very small. There is no need to blindly do questions if you don't learn basic knowledge well. There is no need to engage in "crowd tactics", but we have to do so. In the process of doing the problem, you should be good at summing up, so that you can get twice the result with half the effort. Confucius said: learning without thinking is useless, and thinking without learning is dangerous.
Third, listen to the teacher and be a "good boy".
When a teacher gives a lecture, he must concentrate on the lecture, follow the teacher's ideas and take notes carefully. Many of what the teacher explains in class is the result of his own teaching practice for many years, which can't be found in textbooks at all, but it is precisely these contents that are of great help to cultivate our analytical judgment and reasoning ability.
The time from the senior high school entrance examination has entered the countdown, and time has not allowed us to review ourselves slowly. Teachers help us sum up the problems existing in students' daily study. In addition, they will give us a detailed explanation in their daily lectures based on their years of experience. So we must firmly seize the last chance, follow the teacher and clean up our previous low-level problems. As long as you follow the review steps arranged by the teacher, you can certainly make "steady progress";
Fourth, check and fill in the gaps, and the same mistake can't be made again.
Set up a wrong question book, ranging from homework, mid-term exam, monthly exam, mid-term exam and final exam, collect and sort out all wrong questions in time, make a detailed analysis of each wrong question, find out the crux of the mistake, understand your own weak links, and timely check and fill in the gaps.
When you are free at ordinary times, you can often turn over your own wrong book, recall the changing process at that time, and consolidate the weak knowledge points.
Especially before the exam, there is no need to do many questions. As long as you turn out the wrong questions, you can ensure that all the knowledge involved in the wrong questions is mastered, and "success" is close at hand.
Due to the tight time, some knowledge points may not be involved in class. We can carefully look through our wrong problem books, good problem books and class notes in the past three years to find out our weak links and make up for them by strengthening our memory.
Fifth, it is not impossible to relax.
Never open your eyes until you close them at night. Adults still have "aesthetic fatigue". Don't say we are children. The result will be counterproductive, which may cause aversion to learning. Therefore, we must pay attention to the combination of work and rest, ensure sleep time, work and rest on time, and have a good rest in order to maintain abundant energy and strong fighting spirit. In this state, learning will achieve greater results.
However, "relaxation" is also a science, and you should relax according to your own interests. For example, now you can put some books everywhere at home, you can pick them up after studying, you can browse without reading carefully, which plays a relaxing role and increases a lot of extracurricular knowledge.
Sixth, face the exam with a good attitude.
Liu Yong said: "a person can't be knocked down by the exam, but can only be knocked down by the exam and give up on himself;" If he fails in his later life because he didn't pass the exam, he will not be eliminated by the exam, but by his own' depressed heart'. "So, the exam is a very common thing, but it is only to test how much knowledge you have mastered, so you should treat it with a normal heart.
Sometimes the exam is abnormal and the results are not ideal, which can't affect your study and life. If a good horse stumbles, don't care too much about an exam, because our strength is still there. Don't completely deny yourself because of a mistake. In addition, the problems found in the exam just provide us with a clear direction to improve ourselves. It is better to improve your own shortcomings than to meet them in the real senior high school entrance examination.
For the younger brothers and sisters who will take the senior high school entrance examination next year, confidence is very important. We should believe that anything is possible, make a final sprint and never give up until the last moment.
Seven, maintain enough self-confidence.
We should exchange learning experience and experience with our classmates, treat our shortcomings correctly and give full play to our strengths. Treat all your lessons in a balanced way and don't give up any subject. We must pay enough attention to excellent subjects, strive to improve the slightly weak subjects correctly, and don't invest too much energy in those subjects that we really don't master, so as not to lose sight of one thing and lose sight of another. Establish good self-confidence and believe in your own ability, and you will succeed!
Some learning methods and habits taught by teachers will certainly benefit as long as we stick to them. We don't have to argue with others, but we must argue with ourselves. Only those who "surpass themselves" can truly succeed.
Read (1) ┆ Comment (0) ┆ Reprint ┆ Original Collection (0) 20 10-201Mid-term Mathematics Examination Questions (including answers) of Grade 9 in Haidian District in the school year (20/)
Label: Miscellaneous talk
Reading (19) ┆ Comment (0) ┆ Reprinting forbidden ┆ Collection (0) Untitled (2010-12 23:13
Label: Miscellaneous talk
I've been so busy recently that I haven't been here for a long time. Update! Reading (3) ┆ Comments (0) ┆ Reprinting is forbidden ┆ Collection (0)- Transferred from Shi Hanbing (2010-07-28 21:31).
Label: education
After writing the article "Reading Experience: Thinking about the Second Half", I received letters from some friends one after another, hoping to write more about my reading experience in order to acquire knowledge more efficiently. In addition, the summer vacation is coming, and many parents want to help their children learn, but they don't know how to make their children learn more efficiently. In this article, I will talk about my feelings separately, and it will be very gratifying if it can be useful.
(A) efficient reading methods
Reading is a shortcut to acquire knowledge, active thinking and self-improvement.
When I was a child, I was deeply influenced by my cousin, mainly ancient and modern literary masterpieces. Almost all the books that could be read at that time were literature (literature was the mainstream at that time, writers were the most popular, and some even emphasized their "love for literature" when looking for someone). Because the borrowed books are often in a hurry and read quickly, my fast reading is largely caused by this "reverse mechanism". If I can't return the books on time and lose my reputation, I will face great difficulties in borrowing books in the future. Therefore, we must absorb the knowledge in the book efficiently. The pace of life in modern society is very fast and time is very precious. How to study efficiently in a short time is particularly important.
Now, I basically keep reading two books a week. Before flying, I like to buy a book nearby, read it after boarding the plane, and basically finish reading it when the plane lands.
How to read?
Everyone's situation is different, and the way that suits them may be different, but some regular things may still be close.
I read it like this:
When I get the book, according to the title, think about it first: if I write this book, what kind of views will I have and what kind of ideas will I develop. Then, look at the simple introduction and preface. If the main points of the introduction are the same as your own ideas, and the arrangement of chapters is nothing new, then you can skip this book or just skim it. On the contrary, buy it and watch it. If the author's point of view is novel or close to his own, but the ideas embodied in the chapters are deeper, more systematic and more perfect than his own, then buy it and focus on those chapters that reflect the author's in-depth thinking.
So when I study, I usually look at the catalogue first. A table of contents is an outline and a high summary of the author's thoughts. Understanding the author's general ideas through the catalogue and following the author's ideas will make your ideas and logic more and more systematic, rigorous and clear. Because reading not only gains knowledge, broadens our horizons, but more importantly, broadens our thinking and learns to think more deeply and from more angles.
When reading with a clear framework, you will find that you are no longer passively accepting knowledge, but thinking and understanding the essence of things with the author, and even writing with the author. This will make you feel the uniqueness of the author more clearly, and also help you find the shortcomings or deficiencies of the author. In this way, you can read one book, far exceeding the income from reading ten books in the ordinary way.
Because I knew what I was most concerned about before, and I also knew what I should read roughly and what I should read carefully (of course, I don't know that now, because when the reading efficiency reaches a certain level, I no longer need this choice, and this screening can be done automatically in reading), so I can allocate my time better.
When reading, you must have a pen to draw a line under a wonderful point of view or explanation, or write down your feelings at any time. Because, while reading other people's opinions, you are actually talking to the author. Note that reading is a dialogue with the author! You will naturally have some feelings, and it is very, very important to record them. When you form this habit, you will find that your knowledge acquisition speed will be faster, your efficiency will be higher and your thinking will be more active. It is important to note that you should not reject your own views that you hate very much. As long as the other person can justify himself, you might as well understand. The limitation of China people is: they will think that their views that are quite different from their own are absurd! Often condemn from the moral level, and completely ignore each other's logical relationship. In fact, absurd views are not necessarily unreasonable. We should learn to make the truth more and more clear through communication and debate, instead of making the topics that could have been discussed more and more vague through emotional venting. Everyone has this problem to some extent. I am also trying to correct this shortcoming of myself.
I work in the Securities Journal, and the securities industry is a melting pot. My work involves not only securities, investment, wealth management, finance, mergers and acquisitions, but also macroeconomics and microeconomics. My knowledge of finance, finance, taxation, welfare, real estate, architecture, land, industry, agriculture, demography, new energy, trade, transportation, resources, environment, society, humanities, history and so on forced me to read extensively and efficiently.
I'm using the combination reading method now. That is, several or even a dozen books on the same subject are read together. This is just like holding a symposium, where each author expresses his own opinions, and the opinions of these authoritative people collide or supplement each other, so that you can have a deeper and more comprehensive understanding of the nature of this issue. This way of reading is my favorite! But it is inconvenient to travel. After all, a pile of books is heavy.
Reading is extremely important. Especially the students nowadays.
To tell the truth, China's universities are tireless in destroying people, and many excellent children are gradually eliminated in such an environment. The present educational methods and corrupt environment are all aggravating the destruction of outstanding talents. Therefore, several influential people I know in China did not send their children to such an environment to destroy them, but educated them themselves or sent them abroad to study. This sad and helpless choice is a microcosm of today's reality. How to overcome this? Read! If a child can persist in reading and swim in the sea of books in such an environment, then he will become better, not destroyed.
Knowledge is hardware. No matter how beautiful the education is, it is just a dead letter if it is not based on real talent and practical learning.
Relatively speaking, children who have received education abroad know more about the importance of learning. In my recent speech, I met graduate students from abroad every time. Through this way of communication, they obtained refined and highly summarized knowledge. This is also a shortcut.
Of course, in this impetuous era, inferior books are flying all over the sky. Choosing books is also very important. I especially hate the way of quoting leaders' speeches to prove my point of view, which is very common in China's economics books. This is actually a manifestation of the depravity of intellectuals. Economics can provide new ideas, references or guidance for decision makers, but it is absolutely impossible to demonstrate the correctness of economics through leaders' speeches. This in itself is a kind of putting the cart before the horse. Because many leading cadres actually don't understand economics, and even completely violate the most basic principles of economics. Economists should have pointed out its absurdity and guided it back to the right path, but today's economists are more echoing, proving that the leadership's decision is wise, far-sighted and correct through their own economic knowledge. As a result, some mistakes went further and further. Degeneration to flattery is a sad symbol of the enslavement of intellectuals in this era. Therefore, when the policy of saving real estate came out at the end of 2008, not only a few people, such as the Three Musketeers, pointed out its harmfulness, but more people were calling for three cheers. With the economic development today, policy makers have to find out painfully that they have pushed themselves to a dead end. Some mistakes can only be made once, or only once. When I sighed in June 5438+October 2009 10 that "no one can save China's economy after half a year", who can know the bitterness and helplessness in my heart (see: clip of Shi Hanbing's speech on "What should China do?" on October 9, 2009)!
Therefore, I prefer reading books written by foreigners. Most of their academic research is relatively independent-at least for us-and their books are very clear-cut. Reading such books is a great pleasure. However, it was later learned that even the translated books had been tampered with. For example, a book on the principles of economics, which mentioned the coal mine disaster in China, was deleted. Most of what we see are clean copies (ie castrated). I have to sigh: learning foreign languages, especially English, is very important! In this case, you can easily read the original. Besides, speaking a foreign language is more respected than speaking your mother tongue in this country.
(2) Let children enjoy reading.
For parents, it is a very headache for children to be unwilling to study now.
Children prefer watching TV and movies with dialogues and pictures. Some family members think that children can acquire all the knowledge in this way without reading. This is a very, very wrong understanding.
Reading, movies and TV can never replace each other!
What are the children's specialties? Energetic, imaginative and imaginative.
Movies and TV can really help children understand the outside world, but its limitations are also very obvious-it is easy to stifle or limit the imagination that children need to activate and grow most to a certain extent, because children have been given everything in the picture and do not need imagination. Imagination is the key prerequisite for children to cultivate their thinking ability! Film and television should be used as a way for children to acquire knowledge and broaden their horizons, not all.
I remember when I was a child, my father who went to work in other places brought back a radio. That radio opened a rich world for me. Stories, storytelling, etc. There are no pictures on TV on the radio, but when you listen, the corresponding pictures and scenes will naturally come to your mind. For example, listening to the biography of Yue Fei, even those tragic war scenes can emerge. The information you hear is very beneficial to your child's imagination and thinking ability. My composition was better in primary school, which was related to my habit of listening to books and reading.
When children are painting or playing, or before going to bed, turn on the stereo and play stories, so that children can absorb nutrition imperceptibly. Children's imagination will make up for the defects of words and sounds. After listening to it several times, the child can even tell the story completely, even the tone is very vivid. This way of listening to books is extremely beneficial to the cultivation of children's language and logical ability and memory. Of course, when children perfectly retell the stories they have heard, they must be given enough praise. Praise should not be too hypocritical, but must be sincere.
The same is true of reading. Books are not necessarily gorgeous, as long as there are phonetic symbols, children can read slowly. For children, no matter how beautiful the picture is, it is not as perfect as he imagined!
Parents should never be indifferent to the books their children read. You should attach great importance to it, at least when children think you are important. You should read the book thoroughly before the children read it, so as to exchange ideas with them. This kind of dialogue can not only broaden children's horizons, improve their cognitive ability and psychological quality, but also improve their interest. It is also a kind of happiness for parents. Some of the children's views are often surprising and amazing because they are not subject to any restrictions! Now think about it, how grateful I am to my parents and grandparents. No matter how busy they are, they will never ignore my problems. Although their knowledge is limited, their simple thoughts of peace and kindness have benefited me all my life.
Never buy some books and throw them to the children. Give your child a task to finish reading them in a few days. This way of treating adults has no benefit except that it arouses strong resentment from children. Children's learning efficiency comes entirely from interest. If parents want their children to read a book, they should "accidentally" talk about it many times before buying it. When the child's curiosity is hung up, you don't have to worry about the rest.
Children nowadays are very poor. Scores have long killed their nature, as well as their childhood, happiness and future. Talking about grades in front of children is the fastest way to ruin children! Never talk about grades in front of children. This will seriously distort the child's heart and make his endurance more and more fragile. Children are very competitive, usually work hard and don't talk about grades. Their weariness of learning is often the result of unbearable pressure. Parents should share happiness with their children and let them learn knowledge in happiness. I have read more than 20 books on children's education written by foreign experts, all of which emphasize the importance of happy learning. Even, they think that children working full-time is happiness, and how to have fun is the foundation of education. This is difficult for China people to understand. Foreign junior high school textbooks (such as mathematics) are not as difficult as our fifth grade, but this does not affect them to cultivate a large number of world-class talents, and those of us who are good at exams are so at a loss when we go to the world.
Examination-oriented education makes our nation's thinking more and more limited and rigid. In addition, the transformation from materialism to money-only theory, with the help of the speculative system with real estate as the core, completely destroyed our nation's creative ability and positive mental outlook.
The children are poor. Wise parents should not continue to add pressure to their children and cooperate with external forces to hurt their growth, but should create a relatively relaxed growth environment for their children as much as possible. In this environment, children will gradually become interested in reading.
In addition, it is also very beneficial to take children out for a walk and broaden their horizons during the summer vacation. Don't just take photos when traveling, but pay attention to feel the beautiful scenery, broaden your horizons and exchange ideas with your children. Joshua, an American, once wrote an article that moved me very much. He wrote: "It seems that people in China are unwilling or unaware of the beautiful scenery when traveling. When they arrive at a scenic spot, they all take pictures of each other ... and then leave quickly. China people seem to be doing things there instead of enjoying the beautiful scenery. " China people will not enjoy life more and more. At this point, we should learn from children. Children will enjoy it and have fun, and too many photos will make them disgusted.
As the old saying goes, it is better to study for ten years than to listen to you. If you have the opportunity to bring your child into contact with some people or people with expertise and influence in a certain field, it is also a very rare way to let your child get a subtle influence. The influence of this good atmosphere on children may last for a lifetime. Children are more likely to be motivated to learn from people they have come into contact with and surpass them. This is the reason for the "Three Major Movements in Meng Mu"! Of course, bringing children too much contact with people with bad habits will also make them unconsciously accept the influence of those bad gas fields, which may also accompany them for life. Parents who bring their children into contact with people without discrimination and screening should pay special attention to this. People's aura is something that science is difficult to prove, but many people are really influenced by it.
For children, the problem of reading is not reading itself, but society. This cannot be solved in this paper.
In addition: tonight, Germany plays Argentina, and my two favorite teams meet. As a result, the old horse left sadly, while Aunt Merkel and the graceful Loew laughed like children. Germany's nearly perfect cooperation, strict defense, strong will and indomitable spirit have made it brilliant. The performances of South American teams Brazil and Argentina in this World Cup were disappointing. Their failure proves that no matter how many stars can win without teamwork spirit. Support Germany to win the championship! )
Reading (7) ┆ Comments (0) ┆ Reprinting is forbidden ┆ Collection (0) 20 10 Beijing Senior High School Entrance Examination Math Test Answers /2009 Beijing Senior High School Entrance Examination Math Test Results (20 10-06-27 10:20
Label: 20 10 Mathematics Education for Senior High School Entrance Examination
20 10 Beijing senior high school entrance examination
Math test
School: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
examination
grow
must
know
1. This test paper is ***6 pages, with * * * 5 big questions and 25 small questions, with full marks 120. Examination time 120 minutes.
2. Fill in the school name, name and admission ticket number carefully on the test paper and answer sheet.
3. The answers to the test questions should be filled in or written on the answer sheet, and the answers on the test paper are invalid.
4. On the answer sheet, multiple-choice questions and drawing questions are answered with 2B pencil, and other questions are answered with black pen.
Please return the test paper, answer sheet and draft paper together after the exam.
First, multiple-choice questions (32 points for this question, 4 points for each small question)
There are four options for each question below, and only one of them fits the meaning of the question.
The reciprocal of 1 and -2 is ()
a、B、C、-2 D、2
A: A.
Difficulty: easy.
Test knowledge points: countdown.
The knowledge points frequently investigated in this question are: reciprocal, reciprocal, absolute value, square root and arithmetic square root.
2.20 10 On June 3rd, China's first manned space flight test "Mars -500" was officially launched, including China volunteer Wang Yue.
Six volunteers embarked on a 12 480-hour "trip to Mars", and 12 480 was expressed as () by scientific notation.
a、 12.48× 103 B、0. 1248× 105 C、 1.248× 104 D、 1.248× 103
Answer: c
Difficulty: easy.
Investigating knowledge points: scientific notation.
3. As shown in the figure, in △ABC, point D and point E are on the sides of AB and AC respectively, and DE‖BC. If AD: AB = 3: 4 and AE=6, then AC is equal to ().
a、3 B、4 C、6 D、8
Answer: d
Difficulty: easy.
Test knowledge points: triangles are similar.
4. If the length of the two diagonal lines of the diamond is 6 and 8 respectively, the circumference of the diamond is ().
a、20 B、 16 C、 12 D、 10
A: A.
Simple program: simple
Test knowledge points: the nature of the diamond: the diagonal of the diamond is divided vertically, and the four sides of the diamond are equal.
5. Randomly select a number from the ten numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and the probability that the selected number is a multiple of 3 ().
A, B, C, D,
Answer: b
Difficulty: easy.
Investigate knowledge points: probability.
6, the quadratic function into a form, the result is ()
A, B, C, D,
Answer: D.
Difficulty: easy.
Investigating knowledge points: Formulating the general form of quadratic function as.
7. 10 Students play basketball in teams A and B. Their heights (in centimeters) are shown in the following table:
Team member 1
Team member 2
Team member 3
Team member 4
Team member 5
Team a
177
176
175
172
175
Team b
170
175
173
174
183
Let the average height of the two teams be 0 and the height variance be 0, then the following relationship is completely correct ().
A =, B =,
c、D、
Answer: B.
Difficulty: easy.
Test knowledge points: mean and variance.
Two groups of data that are often investigated in this question: ① mode, median and average: they reflect a group of data concentration trends;
② Variance and standard deviation: They reflect the fluctuation of a set of data, and the smaller the fluctuation, the more stable it is.
8. In art class, the teacher asked the students to cut the white paper shown on the right along the dotted line, and form a bracket with the cut paper and the shadow on the white paper.
Body model, and then put it on the desktop. Only one of the following four schematic diagrams meets the above requirements, so this schematic diagram is ()
Answer: B.
Difficulty: medium.
Inspection knowledge points: the graphic transformation of a square is mainly to inspect the imagination of three-dimensional graphics.
Two. Fill in the blanks (the score of this question is *** 16, and the score of each small question is ***4).
9. If the square root is meaningful, the value range of x is _ _ _ _ _ _ _.
Answer:
Difficulty: easy.
Investigate knowledge points: the square root of quadratic form is greater than or equal to 0 and the solution of unary linear inequality.
10, decomposition factor:.
Answer:
Difficulty: easy.
Investigate knowledge points: factorization.
Key words: there are three ways to decompose factors: one is to extract common factors, the other is to use formulas, and the third is to use cross multiplication. Give priority to the common factor when doing the problem.
Method, and then consider the formula method, if it is two terms, consider the square difference formula, if it is three terms, consider the complete square formula and cross product.
1 1, as shown in the figure, AB is the diameter ⊙O, the chord CD⊥AB, the foot is the point E, and OC is connected. If OC=5, CD=8, AE = _ _ _ _ _ _ _
Answer: 2.
Difficulty: easy.
Investigating knowledge points: vertical diameter theorem.
12 as shown in the hand chart, mark the letters a, b, c and d between each finger, please press the direction indicated by the arrow in the figure (i.e.
Positive integer 1, 2, 3, 4, ...
When the number reaches 12, the corresponding letter is _ _ _ _ _ _ _ _; When the letter C appears 20th1time, the exact number is _ _ _ _ _ _ _ _ _; When the letter c is 2n+ 1.
When it appears (n is a positive integer), the exact number is _ _ _ _ _ _ (expressed by an algebraic expression containing n).
Answer: B, 603, 6n+3.
Difficulty: medium
Inspection knowledge points: routine questions. This question is the simplest one in standard questions over the years.
Iii. Answer the question (30 points for this question, 5 points for each small question)
13, calculation:
Answer:
Test knowledge points: negative exponential power, zero exponential power, absolute value of special angle and trigonometric function value are combined into one question.
14, solving the fractional equation:
Answer:
Difficulty: easy.
Investigate knowledge points: solve fractional equations, and pay attention to: be sure to check the roots.
15. it is known that points a, b, c and d are on the same straight line, EA⊥AD, FD⊥AD, AE=DF, AB=DC. Proof: ∠ACE=∠DBF.
Answer: Prove △ AEC △ DFB
Difficulty: easy.
Test knowledge: triangle congruence.
This topic mainly investigates five methods to prove triangle congruence: SSS, SAS, AAS, ASA, HL.
16. It is known that a quadratic equation with one variable about x has two equal real roots. Find the value of m and the root of the equation.
Answer:.
Difficulty: easy.
Investigate knowledge points: the discriminant of the root of a quadratic equation and the solution of the equation.
17. Solving equations or the application of equations: In 2009, the total water consumption for production, operation and domestic use in Beijing was 580 million cubic meters, including domestic water consumption.
The domestic water consumption is 600 million cubic meters more than the production and operation water consumption. How many billion cubic meters of water are used for production, operation and household?
A: The production and operation water consumption is 65.438+0.3 billion cubic meters, and the domestic water consumption is 450 million cubic meters.
Summary: Yi.
Investigate knowledge points: list one-dimensional linear equations or two-dimensional linear equations.
18, as shown in the figure, the straight line intersects the X axis at point A and the Y axis at point B.
(1) Find the coordinates of point A and point B.
(2) Make a straight line passing through point B, with the X axis intersecting point P, let OP = 2OA, and find the area of △ABP.
Answer: (1) (2)
Difficulty: easy.
Test knowledge points: the coordinates of the intersection of the linear function with the X and Y axes, and the area of the triangle.
Note: There are two situations in the second question. Pay attention to the classification and discussion of ideas.
Iv. Answer questions (20 points for this question, 5 points for each small question)
19, as shown in the figure, in trapezoidal ABCD, AD‖BC, AB=CD=AD=2, BC=4, find the number of times of ∠B and the length of AC.
Answer: ∠ B = 60, AC=
Difficulty: easy.
The test of knowledge points: the practice of trapezoidal auxiliary lines.
The method of trapezoidal auxiliary line: 1. Vertical to the outsole from both ends (this method is the key method); 2. Translating the waist; 3. Translating obliquely.
Line, the fourth is to use a special angle as the vertical line.
20. As shown in the figure, in △ABC, D is a point on the side of AB, and ⊙O passes through D, B, C, ∠ Doc = ∠ ACD = 90.
(1) Verification: The straight line AC is tangent to ⊙ O.
(2) If ∠ ACB = 75 and the radius ⊙O is ` 2, find the length of BD.
Answer:
Difficulty: easy.
Test knowledge points: tangent judgment theorem and property theorem of circle.
(1) Verify Tangent