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300 sats \ 1 reply \ @Scroogey 27 Oct 2024 \ parent \ on: [Daily puzzle] Find the ratio science
Ah, yes!
The two green c 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 \frac{45°}{2}.
Now the inscribed angle theorem says \theta = 3*45°.
Therefore, \frac{r}{k} = \sqrt{2-\sqrt{2}} \approx{0.76537}
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1 sat \ 0 replies \ @south_korea_ln OP 27 Oct 2024
I have \frac{\sqrt{2+\sqrt{2}}}{\sqrt{2}+1} which also \approx 0.76537 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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