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 D is on the diagonal AB of the square. Hence AB is a diagonal of the circle and thus its length of 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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