small square diag is 2*sqrt(2) (Pythagoras)
large square diag is 4*sqrt(2)
distance from small square corner to lower left large square corner is R+x
x = sqrt(2)*R (Pythagoras)
-> 4*sqrt(2) = 2*sqrt(2) + R + sqrt(2)*R
solve by R: R= 2*sqrt(2) / (1 + sqrt(2)) = 1.17
small square diag is 2*sqrt(2) (Pythagoras)
large square diag is 4*sqrt(2)
distance from small square corner to lower left large square corner is R+x
x = sqrt(2)*R (Pythagoras)
-> 4*sqrt(2) = 2*sqrt(2) + R + sqrt(2)*R
solve by R: R= 2*sqrt(2) / (1 + sqrt(2)) = 1.17
I copied the entire thing a d fed it to Chatgpt. I will post the result below and let me know if got is still dumb
Step 1: Key Observations
The circle is tangent to all sides of the large square and the smaller squares.
The center of the circle is at the intersection of the diagonals of the two smaller squares.
The center of the circle is halfway along this diagonal, so the distance from the center of the smaller square to its corner is .
R = 2 - \sqrt{2}.
Final Answer:
R = 2 - \sqrt{2} \approx 0.586
Far from sure, but:
4×√(2)÷4×√(2+1)÷2 =
1,2247448714
The radius of the circle is square root of 2 (approximately 1.4142).
Upon checking again, this is the correct answer.
the answer is 1 😀
nice✌✌