Learning about the 9 point circle - Introduction to Geometry

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Hi remember me, you were a lifesaver last time.Bro can you please tell me once again (if you know) where can I get the complete solution of this problem, somewhere (like Aops..)

Suppose K>=2 and let A1, B1, A2, B2, ...., Ak, Bk be 2k integers such that |AiBj-AjBi|=1 for any 1<=i<j<=k.
Determine the maximum possible value of k.

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Magnificent...

I am suddenly clueless when seeing so many lines intersecting each other. I don't know which will correspond to which, or which will be equals to which.
And that is so great that I can see the thought process of the geometric invention, (or formulation precisely). Wish I would be more "conscious" whenever I encounter such rolling yarn in front of me.
And thank you very much.

If I may suggest, just for the improvement of your channel, such that you will have more viewers.
1. Can you please highlight the thought checkpoints, popping up on the screen, so we can always track down to your elaboration each time we get confused. To be honest, not everyone is as gifted as you, so our thoughts may get blurred sometimes.
2. Perhaps, channel : Flammable Maths could be a good reference to enhance your stream further. You have a really strong points of math observations that we can learn from you. But some, may need entertainments. And it happens that Flammable Math also features the competitive math as one of discussed topics on his channel. So, IMHO it could be a neat benchmark for your channel.
3. If we may, can we know your name and where are you from? Of course you have ever competed in IMO. I remember I have seen your face on a leaflet of math olympiad 2009. Is that correct?

Keep up the pleasant contents. I will always look forward to seeing lessons from you. I wish you have started the channel when I was still competing....

irhamma