Become a master from now on

Chapter 185 Apollonius Circle (ask for a monthly ticket subscription!)
The main committee is very confident in the topics it chooses, and the professors from various countries who come up with such topics also have absolute confidence in the topics they choose.

Every year in the IMO competition, there are only a handful of players with perfect scores, which shows how difficult the topics of the math competition are.

In one hour, Fang Chao only completed about half of the second question.

So far, he has spent more than an hour and a half in total, and there are three hours left. It takes less than an hour to solve the second question, so when facing the third question, there are only three hours left. About two hours.

Time is not urgent, but not abundant.

According to Fang Chao's level in the past, it would take no more than half an hour to solve a question at most. For this kind of test question, it took him more than an hour for the second question, which also gave him a great sense of accomplishment.

"I don't know how Fatty, Xiao Zizhan, Chen Qin, Jin Zixuan, and Lin Sheng are doing in the test questions, but don't hold back..."

Fang Chao let himself rest for 5 minutes to ensure that there was no problem with his condition before continuing to answer.

Suppose the Piltover policewoman moves from point B to point C along BPn+200, BC=200, then Dn+200=CX.

If the Piltover policewoman moves to a certain point Z according to any strategy, then Z is on the left side of point C, if point Z is above BC, then ZYCY, if point Z is below BC, then ZXCX, in short, regardless of the skin No matter how the city policewomen move, they all have Dn+200 greater than or equal to CX.

According to Stewart's theorem.

The so-called theorem means that there is a mathematical formula that has been verified. Fang Chao does not need to verify this process anymore, he just needs to substitute the formula.

CX=(AX·CP+PX·AC)/AP-AC·CP=Dn-Dn/200+1Dn+1/2.

初时时，Dn=0，故no=4*10六次方+20010九次方个回合后，总有Dno10四次方+1/2。

That is, Piltover Policewoman cannot guarantee Dno100,

Therefore, after 10 to the power of nine rounds, the Piltover policewoman cannot ensure that the distance between her and Captain Teemo is at most 100.

This is the answer Fang Chao calculated in one hour and forty minutes, which involved various times of altering, thinking, and writing algorithms.

According to the model of "League of Legends", Captain Teemo only brought a Doran Shield when he went out. Police, once you meet him, Captain Teemo will die without a place to bury him, so facing this situation, Captain Teemo cannot stay where he is, even if he doesn’t know how to buy equipment, he may go to the mall to buy six pairs of shoes. Run as far as you can.

Similarly, the idea of ​​​​solving the problem has come, get it done!
But this cannot be used as a standard, it is just an answer with reference to normal thinking.

That's why Fang Chao had more than an hour to solve the second question in the IMO event.

"It's so fun!"

It is indeed the International Mathematical Olympiad!
Every question asked on the field is enough to make people think deeply. The brain cells of these professors are like gods. In order to embarrass these players, they really do everything. It will never be simplistic, so if a player does not have a good psychological quality, it will be very sad.

However, for the players of the national team, this kind of thing can't be regarded as a big deal at all. They are all players selected from every province and city, and finally selected six players from the 63 national training camps. bit out.

These selected contestants have excellent psychological quality, a lot of practice questions every day, and even terrifying sports are waiting for them. physical and mental problems.

It has to be said that the national team has at least eliminated those with poor mentality in terms of cultivating talents.

The two questions cost Fang Chao two hours and 7 minutes in total.

There are still more than two hours to solve the last question.

Therefore, Fang Chao quickly set his sights on the third question on the first day of IMO.

The last question is a geometry question.

What appeared in front of Fang Chao were two circles of different sizes, and they were located in the plane's rectangular coordinate system. They were each related to the x and y axes, deducing the love and hatred between the two circles.

The small dots between the two circles form a triangle with different side lengths, which Fang Chao calls ABC and A1B1C1.

At the same time, Fang Chao described the Euler lines of two triangles, and named the point where they intersect as point P.

After counting for 10 minutes, Fang Chao found that the only points he had were unable to break the deadlock. He had to create more points. Such a complicated situation not only did not trap Fang Chao, but instead allowed him to find a solution among countless points. A crucial clue.

With a flash of inspiration, he resorted to his ultimate move, taking the point P as the circumcircle point, and made three vertical lines, and the three points were collinear, and Fang Chao made the Seymourson line.

But this is not enough!
It's even worse!

This data cannot be used to calculate the final result.

The entanglement of two circles is still not exciting enough.

Then get a little crazy!
war!
Three circles!
Come on! !
People say that there are three women in one drama, so today Fang Chao is three yuan in one drama. Only by making this situation extremely chaotic, can it be possible to win in the chaos and find a chance of life.

So Fang Chao made another circle in addition to the two circles, the Apollonius circle!

This circle is a circle whose diameter is the line connecting the two equinoxes of the inner and outer divisions of the fixed line segment with a constant ratio m:n.

It's just that at the moment when the circle came out, Fang Chao's whole body suddenly became enlightened.

"It really looks like this!"

The professor who made the question does not know which country he is from, but the question he made is extremely tricky. If you don't think of using the Apollonius circle, then you may still have a lot of detours.

But is this really the case?When the Apollonius circle came out, the whole picture looked extremely messy, but in Fang Chao's mind, this was a broad road, leading directly to Rome!Others were still thinking about whether to use a boat or a car, but Fang Chao directly used a random door, and from here he arrived at the end door of the answer in an instant.

"Who can stop me now?"

"Long live the national team!"

Fang Chao shouted in his heart, roaring!
After an hour, Fang Chao calculated the last node using Desargues' theorem. As for the subsequent steps, just substitute the previous data into the final calculation.

After 3 minutes, Fang Chao put down the pen on hand and put it aside.

So far, Fangchao has solved all the three questions of the IMO event on the first day!
Time spent, three hours and ten eight minutes.

The shortest time-consuming record for all completions on the first day!
Of course, it is necessary to ensure that its score reaches 21 points.

(End of this chapter)