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[Daily puzzle] Find the ratio
826 sats \ 8 comments \ @south_korea_ln 26 Oct 2024 science
Previous iteration: #739914 (answer in #739973)
Please let me know if you prefer harder or easier problems. I cannot satisfy everyone with every puzzle but I can at least try to alternate difficulties.
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201 sats \ 5 replies \ @SimpleStacker 26 Oct 2024
Is there a unique solution? This is as far as I got
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21 sats \ 4 replies \ @Scroogey 26 Oct 2024
I got
which seems to be equivalent.
appears to be 3*45°, but I don't know why.
Is twice , the arc length?
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1 sat \ 3 replies \ @SimpleStacker 26 Oct 2024
I didn't read it that way, but I was wondering if the fact that the triangle is right-isosceles imposes some kind of additional condition that lets us find .
Don't really have the time to work it further right now though. Geometry isn't really my forte.
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1 sat \ 2 replies \ @south_korea_ln OP 27 Oct 2024
I need to spend some time myself analyzing your answers, but for , the inscribed angle theorem should help.
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300 sats \ 1 reply \ @Scroogey 27 Oct 2024
Ah, yes!
The two green have equal lengths.
Hence, the angles in the bottom right corner must be equal.
They both add up to 45°, because the triangle is right-isosceles, hence they are .
Now the inscribed angle theorem says .
Therefore,
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1 sat \ 0 replies \ @south_korea_ln OP 27 Oct 2024
I have which also if I'm not mistaken.
Your expression is even simpler.
Good job :)
A GitHub PR for collapsable answers is on its way in next few days. We'll be able to hide spoilers which should increase the fun factor.
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21 sats \ 0 replies \ @Undisciplined 26 Oct 2024
I don't have the bandwidth for this one today, but I do like the harder puzzles.
I'll circle back to check on other people's solutions.
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0 sats \ 0 replies \ @Scroogey 26 Oct 2024
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