Geometry question to test the world's best math students (IMO 2024 problem 4)

Comments · 204

• DE

  @deerh2o · 2 years ago

  I am always so impressed both with the Olympians and the mathematicians who created such intriguing problems. I would enjoy seeing a breakdown of the other problems.

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• DO

  @doscurantismo · 2 years ago

  Please could you upload a video in which you describe the hardest one?<br>Great video as always.

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• ZM

  @zmaj12321 · 2 years ago

  You NEED to cover problem 5!!! The solution is so easy, and I think it would be a perfect video for your channel.

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• AG

  @agytjax · 2 years ago

  Glad to see Presh back to posting challenging and ponder-worthy problems !

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• AL

  @alexandrubivolaru4076 · 2 years ago

  I always understand each step he explains on this channel. I would love to see other difficult problems explained by him rather than anyone else. Hopefully he will &nbsp;solve another IMO problem soon

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• HE

  @hello7538 · 2 years ago

  I can tell how expert geometrists can easily think of this. Firstly, they would see that L and K are midpoints, and immediately take a homothety of 2 centered at A on triangle LIK. After that, they will immediately notice the parallelogram and complete it, since it would fit with point I after the homothety. After that, label the angles on the parallelogram, find which angles are same to the angles that are labeled, and the problem kind of just falls apart. I’ve been into Olympiad geometry for a while, so I somehow just recognize this kind of stuff lol.<br><br>Also, this is an easy geometry problem compared to most out there in Olympiads. Any expert in olympiads will probably agree with this.

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• WA

  @waheisel · 2 years ago

  Wow! I could follow all the steps of the solution, but am glad I quickly gave up on trying to solve this one. I never would have come close!

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• DO

  @Doktor_Vem · 2 years ago

  I honestly feel like this is more of a reading comprehension and visualization excersize than a math excersize

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• 8A

  @8A52shuvroanindyabapari6 · 1 year ago

  Such an elegant solution deserves an ovation

• MU

  @MuhammadFareedRaza · 1 year ago

  I am amazed at this is the easy one question in IMO

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• BI

  @BigYoda毛皮猫 · 2 years ago

  At around <a href="https://www.youtube.com/watch?v=i6dVarRV61E&amp;t=930">15:30</a> you concluded that AI = QI with some good calculations, <br>But couldn&apos;t you also say that becouse:<br>X&apos;Q -&gt; AY&apos; and: AX&apos;-&gt; Y&apos;Q,<br>With a circle midpoint I,<br>And because the circle is in the middle of the square,<br>Which should mean that:<br>AI = QI<br>And<br>X&apos;I = IY&apos;?

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• TH

  @thegreatgreenarkleseizure1994 · 2 years ago

  I have always loved geometry, even though I haven&apos;t &apos;used&apos; this kind of math all that much in life. &nbsp;I find the whole set of concept fascinating, and making proofs was my favorite part of it all. &nbsp;Using rule x to show y is just so fulfilling. &nbsp;All that to say, I had to pause and rewatch a LOT in this particular video, not just because some of the concepts I was either never fully taught, or simply don&apos;t remember. &nbsp;Once I finally followed along with all of the details, it all made perfect sense, and while I certainly could never have come up with this in my own ability, I still got the joy from seeing it all come together.<br><br>On thing though, in the future, when doing all of the angles and showing how they are the same, if you could color or somehow label the angles other than the strict &lt;ABC format, it really helps with those of us who are visual learners. &nbsp;Seeing 𝜃 or 𝜌 or 𝛼 used as labels or the colors like you did a little of (blue, green, red, etc.) is mush easier to comprehend the compared angles and sums. I know it isn&apos;t &apos;math standard&apos; for notation, and I know it isn&apos;t an easy task, but I know I cannot be alone in knowing it would accelerate my full understanding and lessen the number of pause/rewind cycles.<br><br>Thanks for your hard work in keeping all of our minds sharp!

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