There is a simpler solution: write down the Pythagoras theorem for the right-angled triangle made by r, r-1, and r-2. See the figure, even though it's not a good one! Interestingly, the equation obtained at the end is the same as the one obtained immediately here!
2026-08-05 00:09:34
4
dkespo :
r^2=(r-1)^2+(r-2)^2 Gives r=5. So Area=25π
2026-08-06 23:10:49
0
Fadil :
Additionally, for r between 2 and 10 r=5 is the only r that gives integer length of red rectangle. Gave this to chatgpt: For this photo r must be 5 because of intersecting cord theorem. But expanding on that. For every circle in a square. The red rectangle should have a definite length and width relative to r of the square. Let’s (1) develop a formula of length and width relative to r. (2) calculate length and width for r between 2 and 10. And got
2026-08-04 19:18:38
0
Nicolas Mukwaiwa :
👏
2026-08-04 13:58:13
3
MorgothTheFair :
Dang, I went about this all wrong. Ended up with a quartic for r which turned out to have solutions 1, 5 and ±√5 🤨.