RE: LeoThread 2025-01-06 08:15

avatar
(Edited)

You are viewing a single comment's thread:

This is nice one. Solve it, find the radius of the circle, if you believe you are very smart.
#quiz #puzzle #contest
First right answer gets a bOOm.

Plz explain exactly (formula) how did you get your result.

0
0
0.000
12 comments
avatar

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

0
0
0.000
Reply
avatar

The radius of the circle is square root of 2 (approximately 1.4142).

0
0
0.000
Reply
avatar

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

0
0
0.000
Reply
avatar

Let’s directly solve this:

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.

0
0
0.000
Reply
avatar

Step 2: Solve for the Circle’s Radius

  1. The large square has a side length of 4 (since ).
  1. The diagonals of each smaller square measure .
0
0
0.000
Reply
avatar

The center of the circle is halfway along this diagonal, so the distance from the center of the smaller square to its corner is .

0
0
0.000
Reply
avatar
  1. The radius R is the distance from the center of the circle to a corner of the large square, minus :

R = 2 - \sqrt{2}.

0
0
0.000
Reply
avatar

Final Answer:

R = 2 - \sqrt{2} \approx 0.586

0
0
0.000
Reply