MHB Circles in a square and diameter of the circle

Thread starter Wilmer
Start date Apr 30, 2019
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Circle Circles Diameter Square

AI Thread Summary

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.

Apr 30, 2019

Wilmer

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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May 1, 2019

Olinguito

$20(\sqrt2-1)$, easy.

May 1, 2019

Wilmer

No.

diameter = 40(3-2√2) = ~6.86

Not as easy as it appears...

May 1, 2019

Olinguito

You’re right. I overlooked the teeny bit in the extreme corner.

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