Liu Yichen looked at the Mathematical Olympiad textbook. At this time, he was learning the properties of four points in a circle, that is, a circle inscribed in a quadrilateral.

This knowledge point is very rich and covers a large number of knowledge points that are not found in textbooks.

One of the interesting things about the Mathematical Olympiad is that it is based on the scope of high school knowledge points, but it is often difficult to follow the textbooks and follow the textbooks to complete the question types. It needs to be extended and expanded.

For example, to determine that four points are in a circle, connect the four points to form two triangles with a common base, and both triangles are on the same side of the base, proving that their vertex angles are equal. This is the property of the four points in a circle.

The angles of a circle subtended by the same arc are equal. This will not appear in the textbook, but will appear in a question in the after-school exercise book or a proof question in the test paper.

But in the Mathematical Olympiad, it is a knowledge point, and you have to understand and remember it. Only when you are doing questions can you apply it quickly. Otherwise, if you have analyzed a question clearly, the exam time will be over.

And as long as you master the relevant knowledge points of four-point congruent circles, it will also be helpful for ordinary mathematics exams. For some multiple-choice questions and fill-in-the-blank questions, you don’t need complicated calculations. You can get the answers in a few seconds. Just answer the questions.

Once you master the knowledge points, it will be easier for you to answer questions.

For example, four points and a circle can be summed up in four words, and its judgments are only seven. But if you memorize it, you will find that you have memorized it, and when you learn other things, you will forget all of them.

Yang Zhendong and other teachers in the Mathematical Olympiad training class repeatedly emphasized during class that mathematics must be understood and memorized, and it must be learned and applied flexibly. The active part is thinking. They strongly oppose rote memorization. There is a thick textbook and

How can you possibly memorize a large number of exercises?

This requirement is simply more difficult than memorizing the entire Oxford Dictionary.

Even now, Liu Yichen finds it difficult to learn the relevant knowledge of this Mathematical Olympiad, which requires a considerable amount of time and energy.

Among the three major Olympiad competitions of mathematics, physics and chemistry, Liu Yichen's biggest feeling is that the Mathematical Olympiad is the most difficult. He spends as much time on mathematics as physics and chemistry combined, but he still feels that the Mathematical Olympiad is particularly brain-burning.

From nine o'clock to twelve o'clock, Liu Yichen was understanding and mastering the relevant knowledge points of the four-point circle. It only took a few pages, but the amount of knowledge was extremely extensive. The pictures Liu Yichen drew and the formulas on the draft paper exceeded 10 pages.

, and then I felt that I had almost mastered it. I went to the cafeteria to eat something simple, and Liu Yichen continued to work on the Mathematical Olympiad. His next goal was to solve the two theorems of the right-angled triangle midline theorem and the projection theorem.

Right triangle midline theorem: The length of the midline of the hypotenuse of a right triangle is equal to half of the hypotenuse. It is a simple sentence, but it is not simple once it is expanded. It is like a proof question, how to prove this sentence.

This involves the properties of a right triangle. The two triangles are similar. To determine the parallelogram of the quadrilateral formed, through parallelism and equilaterality, we can find that the length of the midline of the hypotenuse of the right triangle is equal to half of the hypotenuse. This proves that the length of the center line of the hypotenuse of the right triangle is equal to half of the hypotenuse.

The median line theorem holds true.

This question is not bad. Connected to it is its inverse theorem. There are several inverse theorems. The first inverse theorem is: in a triangle, it intersects with both sides of the triangle, is parallel and equal to the third side of the triangle.

Half of the line segments are the median of the triangle; the second converse theorem is: within the triangle, the line segment that passes through the midpoint of one side of the triangle and is parallel to the other side is the median of the triangle.

"You idiot, Huanggang Secret Paper is really killing people. They even used proof questions from the Mathematical Olympiad textbook as test paper answers~~" Liu Yichen cursed in his heart, because he had done both the median line theorem of a right triangle and its inverse theorem.

It's not in other test papers, it's in the Huanggang Secret Paper.

Sure enough, this Huanggang secret volume is not a good thing!

If you love him, give him a set of Huanggang Secret Scrolls, that will be heaven; if you hate him, give him a set of Huanggang Secret Scrolls, that will be hell!

After secretly cursing the Huanggang Secret Scroll, Liu Yichen continued to overcome difficulties and came to the projective theorem. This projective theorem is also a sentence: in rt△abc, cd is the height on the hypotenuse, then cd^2=ad*db;ac

^2=ad*ab;bc^2=bd*ba.

In a word, it is a very difficult proof question, and you can take three proofs in one test. This means that you can take three proof questions for the same picture.

This theorem does not appear in the required textbooks, but is fully explained in the high school mathematics elective course 4-1 Geometry Proof. But even so, it often appears in geometry-related proof questions to examine students.

Mastery of knowledge related to geometry.

But even so, many students still make mistakes.

Yes, even if the textbooks are available and you are tested exactly as they are, you may not be able to fully master them.

Therefore, it is very reasonable to say that mathematics is a subject of logic and thinking.

Liu Yichen also took advantage of this opportunity to consolidate his knowledge of projective theorem. This kind of thing is good for strengthening understanding and memory.

"Liu Yichen~~" Just when Liu Yichen was about to continue to further study the triangle angle bisector theorem, a voice rang in his ears.

Liu Yichen knew it was Feng Lin without looking. Liu Yichen took the information back into his bag and looked at Feng Lin. He saw that Feng Lin had black and elegant hair, a light fragrance on her body, no makeup, youthful beauty, and very fair skin.

The water of Jiulong River really nourishes people!

"Feng Lin, let's go~" Liu Yichen said, carrying his bag.

The two walked side by side. As Liu Yichen's height grew to 185cm, Feng Lin, who was not originally short, suddenly looked smaller and more delicate. There was a height difference of more than 20 centimeters between the two.

Some people were talking and laughing, talking about a school team game held yesterday afternoon. This game was a friendly match. Since the school team got the previous bonus, it has also changed from shot to gun. Every member of the school team is unified in sports.

With uniforms and uniform basketball shoes, even basketball is much better than before.

Moreover, school students are more interested in basketball, so yesterday’s friendly match with No. 2 Middle School attracted many students to watch. The two sides fought back and forth. In the end, Liu Yichen used a three-pointer to kill the game and prevent the game from dragging out.

Overtime.

After Liu Yichen's contact with Feng Lin during this period, he knew that this girl was a big fan of the Black Mamba, but he only limited himself to reading basketball magazines and watching NBA games. As for playing basketball, he was pretty bad, and his strength was

Not enough, even when shooting from the free throw line, 9 out of 10 shots are missed. It’s not just empty shots, it’s three-shot misses!
Chapter completed!