Top Student at Their Peak
Chapter 270: 115: When Brother Qiao Gets Serious—Simply Terrifying!_6
Chapter 270: Chapter 115: When Brother Qiao Gets Serious—Simply Terrifying!_6
Yu Wei glanced at Yu Yongjun, then at Gong Jiatao, who still hadn’t come to his senses, and silently took the paper. After looking at the problem, he finally understood how shameless this Little Fatty was.
He actually picked a geometry proof problem…
To be honest, Yu Wei actually liked Yu Yongjun’s shamelessness, but as soon as he read the first word of the problem, Qiao Yu said: “Hold on, read it when we’re in the game, there’s no suspense if we know the problem in advance.”
Yu Wei didn’t say anything and immediately went silent.
It was Little Fatty next to him who couldn’t take it anymore and shouted loudly: “Aah! I can’t take it anymore, hurry up, hurry!”
Saying this, Yu Yongjun quickly set up the room.
Once Qiao Yu entered the game, and as the countdown ended, Yu Wei began to read the problem: “Let D be a point inside the acute triangle ABC satisfying ABAC and ∠DAB=∠CAD. Let E on line segment AC satisfy ∠ADE=∠BCD, and F on line segment AB satisfy ∠FDA=∠DBC.
Moreover, let X on line AC satisfy CX=BX. Let O1 and O2 be the circumcenters of triangles ADC and EXD, respectively. Prove that line BC, EF, and O1O2 are concurrent.”
After reading the problem, Yu Wei couldn’t help but peek at the gaming screens of the two. Qiao Yu seemed to be engrossed in maneuvering his in-game character around Little Fatty’s Arthur under their turret, having chosen Old Master as his hero.
To be honest, Yu Wei thought this hero was rather tricky to duel with, after all, his ultimate can control. But then again, since the ultimate isn’t a lock-on skill, it requires prediction when activated.
Solving a geometry proof while playing a game without errors, at least Yu Wei thought he couldn’t do it.
Just as Yu Wei was pondering how Qiao Yu was handling this, Qiao Yu suddenly said: “Help me draw the diagram according to the problem, then extend EF and draw a line to intersect BC; call the intersection point J.”
Yu Wei, unable to enjoy the game’s spectacle now, obediently sat at the desk, began drawing the diagram according to Qiao Yu’s instructions, and jotted down what he said.
Gong Jiatao stood silently beside Yu Yongjun, watching their gameplay.
“First step, prove Lemma One: B, F, E, C are concyclic. First, draw the circumcircle of triangle ABC and extend AD to M; then draw the circumcircle of triangle BDF… Finally, we get ∠DBM=∠DBC+∠CBM…”
“Wait a second…slow down!” Yu Wei suddenly interjected.
Gong Jiatao was taken aback and looked up…
“Alright, let me know when you’ve finished writing.”
“Okay…”
“…So MB is tangent to the circumcircle of BDF, similarly, MC is tangent to the circumcircle of EDC… According to the power of a point theorem, B, F, E, C are concyclic. Second step, prove circles BDC and EDF are tangent, JD is the radical axis of the two circles…”
“Oh my God, Fatty, give it your all, you got snagged by the ultimate?”
“Can you blame me? I thought my skill could secure the first kill, who knew it wouldn’t be lethal?!”
“You two stop bickering…” Yu Wei couldn’t help but shout.
Qiao Yu was speaking rather fast, and recording everything without errors required concentration. These two quarreling next to him was really annoying.
Wait, did Fatty just get taken out?
Just as this thought flashed through his mind, Qiao Yu spoke again: “Let the intersection of EF and AD be H, from the just-proven Lemma One we know H, E, C, M are concyclic, giving ∠FED+∠DCB=…”
Yu Wei couldn’t afford to pay attention to the game’s progress and started writing furiously…
Seven minutes later: “From Lemma 5, JK=JD, we know J lies on the perpendicular bisector of DK. From Lemma 4, we know D, K are intersections of circle O1 and circle O2, hence DK is the common chord of the two circles, O1O2 is the perpendicular bisector of segment DK, so J is on O1O2, proof completed.”
As Qiao Yu finished speaking, there was a shout from the other side: “Whoa!”
Game over…
Yu Wei didn’t bother writing down the last sentence, there was no need, the previous proof process was already perfect.
Plus, he didn’t need to note it down since the paper he wrote on was now in Gong Jiatao’s hands, who had come over after watching the game.
He certainly knew the difficulty of the problem; it involved power of circles and radical axes, Monge’s Theorem, the Mick Point, inverse transformations, and more… He had come across similar problems, even at the IMO itself.
This left him completely puzzled as to how Qiao Yu could solve this while gaming.
Throughout, Qiao Yu didn’t even need to glance at the drawing he made.
How was he supposed to catch up?!
Watching Qiao Yu sitting quietly, exiting the game on his phone, it wouldn’t be an exaggeration to say that a slight sense of despair crept into Yu Wei’s heart, just as Qiao Yu’s voice reached his ears: “You’re writing it too slow; we could’ve wrapped up the game a good two minutes earlier.”
Yu Wei suddenly felt an urge to curse, when Yu Yongjun’s voice reached his ears: “Damn, what a waste, I didn’t mention we couldn’t surrender just now, huh! If I had surrendered earlier, before completing the problem, wouldn’t that mean I won?”
After hearing this, Yu Wei felt oddly comforted inside.
One must admit, it did seem like a decent solution, at least Qiao Yu wasn’t so invincible as to break rules.
Yu Yongjun’s words even left Qiao Yu a bit stunned.
Having just won a match, Qiao Yu earnestly said: “I really underestimated your shamelessness, this rule must be added, no surrendering in the game. Who’s next?”
“Let me give it a try.” Before Yu Wei could speak, Gong Jiatao piped up.
Watching from the side had made his hands itch, and admittedly, it was quite an interesting game he had never tried before. Plus, he had some suspicion whether the trio was playing a prank on him, trying to get into his head.
After all, during the CMO, he could tell these three got along quite well.
“Aren’t you guys going to check if the problem’s solved correctly?” Qiao Yu asked.
“I just checked, it’s fine, but this time you also have to give me a problem,” Gong Jiatao said.
“Alright!”
“Boss, this time I’ll help with the notes, I write super fast.”
“Let’s have Yu Wei do it, your track record is too unreliable, I don’t trust you with the notes.”
“Oh no, really? Boss.” Yu Yongjun seemed hurt, but Qiao Yu ignored him.
“Use my phone to record.” Yu Wei suddenly said.
“Hmm?” Qiao Yu looked at Yu Wei, his gaze made Yu Wei a bit nervous, so he explained: “I want to watch the game.”
Qiao Yu thought for a moment, then said: “Alright, but make sure to record.”
Yu Wei silently walked over to Gong Jiatao, only to find this guy looking a bit peeved…
Of course, Yu Wei knew it was because of his earlier comment about wanting to watch the game, which wasn’t exactly supportive, but it didn’t matter.
He’s just a little impressed by Qiao Yu for now.
Who does this Beijing fellow think he is? Just a CMO contestant who got a bit lucky, that’s all.