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567 sats \ 5 replies \ @SimpleStacker 11 Oct \ on: [Daily puzzle] Find the radius of the circle science
Ok, for real this time. Let
We know
Moreover, it'll be useful to write:
The angle of the "pizza slice" that the green region covers is:
The area of the pizza slice is
Thus:
Or:
Which gives
I'm pretty sure I had the same answer, but I was trying to work it out analytically.
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I'm not as much of a fan of these brute force calculations, but once I start on something I find it very hard to stop...
I gave myself 15 minutes to do this, and I thought I had it, but it turns out I made a mistake. Ended up spending maybe 30-40 minutes on this problem... not great for my productivity today lol
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I don't think it simplified nicely, which isn't surprising when you put stuff like that into an inverse cosine.
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Yeah, i also usually prefer the ones that simplify nicely. Also because it's an indirect confirmation one is on the right track.
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It feels like a better puzzle when the answer comes out nice and simple.
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