Circles in a square and diameter of the circle

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Discussion Overview

The discussion revolves around the geometric relationship between a circle inscribed in a square and a smaller circle that is tangent to both the larger circle and two sides of the square. The specific question posed is to determine the diameter of the smaller circle when the square has sides of length 40.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant describes a scenario involving a larger circle inscribed in a square and a smaller circle tangent to both the larger circle and two sides of the square.
  • Another participant suggests that the problem may not be as straightforward as it initially seems, indicating potential complexities in the geometric relationships involved.

Areas of Agreement / Disagreement

There is no consensus reached among participants regarding the simplicity or complexity of the problem, and the discussion remains unresolved.

Contextual Notes

The discussion does not provide specific mathematical steps or assumptions that may be necessary to solve the problem, leaving certain aspects open to interpretation.

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.
 

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