Circles in a square and diameter of the circle

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SUMMARY

A circle inscribed in a square with sides measuring 40 units has a diameter of 40 units. A smaller circle, tangent to the larger circle and two sides of the square, is inscribed in one of the corners of the square. The diameter of this smaller circle can be calculated using geometric principles, specifically the relationship between the radius of the larger circle and the dimensions of the square. The diameter of the smaller circle is determined to be 20 units.

PREREQUISITES
  • Understanding of basic geometric principles
  • Knowledge of inscribed and tangent circles
  • Familiarity with square dimensions and properties
  • Ability to perform geometric calculations
NEXT STEPS
  • Study the properties of inscribed and tangent circles in geometry
  • Learn about geometric constructions involving circles and squares
  • Explore advanced geometric problem-solving techniques
  • Investigate the application of geometric principles in real-world scenarios
USEFUL FOR

Students of geometry, educators teaching geometric concepts, and anyone interested in solving geometric problems involving circles and squares.

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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