It has been 1 month since the biggest Mathematics Olympiad in the world, named IMO (International Mathematics Olympiad) has been held virtually (due to COVID-19, of course) from 19th to 28th September 2020. This year, Russia acted as the organising country for this prestigious event for high schoolers all around the world. Frankly speaking, whenever this moment comes in each year, I always take a moment to be quite nostalgic about the last time I participated in this very same olympiad (which is actually 7 and 8 years ago. Yes, I participated twice in this olympiad).
For some background, the format of this competition is that each participant needs to tackle 6 problems, divided into 2 days (so each day has 3 problems, and the problems are sorted based on difficulties for each day). Therefore, problem 1 and 4 are always the easiest in each day, followed by problem 2 and 5, and lastly the most difficult problems for each day are problem 3 and 6.
For this year, I took some interest in the problem 1, since it's Geometry (yeah, after I participated in IMO for the first time, I somehow took interest in studying Geometry further, and later on I can say this field is the strongest field I master among 4 available fields in IMO). Here are the problems.
First thing that came to my mind while reading this problem is that... wait what? 1:2:3? It's quite intimidating for me somehow, since, well, how can you accurately draw such picture, given that you're only allowed a ruler and proctor during exam? Due to me being intrigued, I finally took a challenge upon myself to try drawing the picture really accurately. Though at last I succeeded in around half an hour in doing so, I was made quite disappointed that the problem itself took much shorter time to solve than for me to draw its picture.
Yeah, after the drawing is made, somehow everything became so obvious that it took me around 10-15 minutes to finally came up with the solution. How long does it take to write down the complete one? I dunno, since, well, I was not participating in this year's competition after all hahah...
Or perhaps, since I drew it in certain way that everything became so obvious? I'm not really sure, even now.
Anyway, here is the picture that I made for this problem. It may look very complicated but it's just because there are lots of circles involved.
Hopefully the picture makes quite some sense, since it's quite tricky to come up with the picture as accurate as this one, given the problem.
And in my opinion, I think this is the first time I faced such problem in which drawing its picture takes much more challenge than actually solving it. It's such a fantastic ride, actually, to finally be able to come up with this beautiful picture (feels suddenly like Picasso hahah).
And to solve the problem itself? Well, it will come in another post (if I'm not that lazy lol). But seriously, everything became much more obvious given that picture.
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