Who is asking: Other
Level: Elementary
Question:
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.
bob
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
Hence
2 |BC|2 = 602 = 3600
and therefore
|BC|2 = 1800.
Taking the square root on my calculator I get
|BC| = 42.43
Penny