MHB Circles in a square and diameter of the circle

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The problem involves a larger circle inscribed in a square with sides measuring 40 units. A smaller circle, tangent to the larger circle and two sides of the square, is placed in one corner of the square. The challenge is to determine the diameter of this smaller circle. The solution requires understanding the geometric relationships between the circles and the square. The problem highlights the complexity of seemingly simple geometric configurations.
Wilmer
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A circle is inscribed in a square with sides = 40.

A smaller (of course!) circle tangent to the above
circle and 2 sides of the square is inscribed in
one of the corners of the square.

What is the diameter of this circle?
 
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$20(\sqrt2-1)$, easy.
 
No.
diameter = 40(3-2√2) = ~6.86
Not as easy as it appears...
 
You’re right. I overlooked the teeny bit in the extreme corner.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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