On March 4th, the first stage of the Mathematics Olympiad National Training Team officially began.

In addition to today, there will be four exams on March 5th, March 8th, and March 9th.

There are three questions in each exam, and the time of the exam is 900-1200 in the morning.

In the time outside of the exam, some professors will give lectures to students, mainly to break through some difficult problems and sort out the knowledge.

In the afternoons and evenings of each day, there will be their own self-study time, where students can study and discuss or do some mock questions.

There is plenty of time, at least for Su Mu, it is equivalent to going out for a trip at public expense, eating and drinking for free.

I walked into the examination room with a relaxed mood and took a sip of Nongfu Spring.

Today's weather is very good, and it is another day full of energy.

It's just that after sitting down and looking around, Su Mu didn't know how to describe his current mood.

"Four invigilators is a bit excessive."

Because the number of candidates in the training team itself is relatively small, the 60 students are divided into three examination rooms, each with 20 people.

However, in Su Mu's examination room, there are four invigilators before and after!!

Three male teachers, one female teacher, and the female teacher has been looking at her mobile phone screen and looking in the mirror from time to time!!

Not only that, but there is also a patrol examination team outside the door, and they always cast caring eyes.

Su Mu seriously suspected that these teachers just came to invigilate the exam because they had nothing to do, this is already the level of IO's exam, who can make this kind of question, who still helps with such a little trick as cheating?

These difficult questions, let alone students, I'm afraid some teachers may not be able to do it!!

The test papers were distributed one after another, and Su Mu retracted his cranky thoughts.

It didn't matter to him how many invigilators there were, and he just wanted to get into the groove as soon as possible.

"It's all short questions."

Seeing the questions on the test paper, Su Mu was slightly stunned.

The first is the geometry of a circle, the second is a sequence, and the third is an equilateral array of triangles in the inverse Pascal triangle.

There are not many conditions given, but from Su Mu's direct point of view, the difficulty should not be small.

A smile spread across his face.

He had been studying the poetry conference before, and he hadn't taken such a high-intensity exam for a long time.

Although he had already trained before, the usual training was still different from the examination room after all, and now he suddenly entered this state, and Su Mu suddenly felt a sense of nostalgia.

"The first problem is shown in the figure, it is known that Y is the circumscribed circle of the acute triangle ABC, D and E are respectively on the line segment AB and AC, and the perpendicular bisector satisfying AD=AE, BD, and CE intersects the inferior arc AB and AC in F and G respectively, proving that DE and FG are parallel or coincide."

The first geometry is a little less described than expected.

Su Mu thought about it carefully, and was just about to start drawing again by himself, but the tip of the pen suddenly stopped.

"This question? Is it that simple? Several question marks rose in Su Mu's mind.

I read the question carefully again, and the puzzled expression on my face became even heavier.

He even began to wonder if he was too awesome himself, or if the subject was too simple.

"This question can be answered directly using Archimedes' string theorem."

Archimedes' theorem is an entry-level theorem in Archimedes' mathematical theory, in which the projection of the midpoint of the two arcs of two arcs composed of two strings of different lengths in a circle on a longer string is the midpoint of the broken string.

In mathematical language, it is a folded string of a circle formed by ab and bc, ab&a;a; ap; gt; BC, which is the midpoint of the arc ABC, F⊥AB, and the perpendicular point is F. then af=bf+bc.

In this problem, you only need to make auxiliary lines, and you can directly apply this theorem!

"It can't be that simple, right? This is a training team. ”

According to Su Mu's rating for this question, at most it is the difficulty of the provincial competition, as long as there are Olympiad students with a certain mathematical foundation, they can answer it.

Now I'm going to enter IO, why is it so easy to take the test?

Could it be that there is a trap in this question, and I want them to prove Archimedes' theorem?

But even so, it is quite simple to prove Archimedes' string theorem, because it has already been foreshadowed by predecessors, and it can be proved quickly by using the method of complementing the short truncation.

After struggling for seven or eight minutes, Su Mu changed four or five methods, and finally determined one thing.

This question is a "true score question".

"Let the midpoint of arc bc be k, and take the point x on arc bc, y so that bx=cy=ad=ae."

"From Archimedes' string theorem, f is the midpoint of the arc xba, g is the midpoint of the arc yca, and the arc bx = arc cy."

"So, ∠fak+∠afg=1/4(arc agy + arc afx + arc xky) = 90"

"Therefore, FG is perpendicular to AK, and it is proved that FG and DE are either parallel or coincide."

In the process of solving the problem with a total of four sentences, even Su Mu felt that he had written too little.

Or.

Write more water words??

I always feel like I've written too little, and I'll be deducted points.

Su Mu sighed.

He wished the questions were more difficult.

This kind of simple thing can really make people feel uneasy.

I thought it was the title of the glory king, but it turned out to be a bronze three, and the contrast was too great.

It's too bad to give him Su a certain face!

The second question is not very difficult either.

Su Mu only took about 20 minutes to give an answer.

The third topic is about equilateral triangle arrays of inverse Pascal triangles, which is a little more complicated.

However, judging from Su Mu's current level of mathematics, it is simply a scoring question! It still took less than half an hour to write the process.

It's only four minutes past ten o'clock, and Su Mu has completed today's exam!!

"The questions are so simple, it's no different from ordinary monthly exams."

Su Mu held a pen in one hand, his face full of regret.

He's ready to make a big deal.

Unexpectedly, the selection of the first question directly gave him a "fright".

Before, he also felt that this kind of difficult topic could not be done by ordinary teachers.

But now, Su Mu has no idea of this!

Today's three questions are too easy!

Even his Xiaoke can do a full score when he comes over, okay!

It's clearly not as difficult as the training questions they did last night!

I looked up again and looked around.

Su Mu was still very puzzled in his mind.

Because there are no other candidates who have completed the question except himself, this has to make him revisit the question.

Could it be that there is something I haven't taken into account??

Why hasn't anyone else done it?

。