Quandaries and Queries


Who is asking: Other
Level: Elementary

my granddaughter asked
what is the largest size square in inches
would fit in a 60 inch circle?
I believe it to be around 42.3 inches but
would like to teach her how to do it mathematically.



Hi Bob,

The argument requires the Pythagorean Theorem. Draw a circle with a square, as large as possible, inside the circle.

By the symmetry of the diagram the center of the circle is on the diagonal AB of the square. The length of AB is 60 inches and the lengths of BC and CA are equal. The Pythagorean Theorem then says that

|BC|2 + |CA|2 = |AB|2


2 |BC|2 = 602 = 3600

and therefore

|BC|2 = 1800.

Taking the square root on my calculator I get

|BC| = 42.43




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