Question 812370
<pre>
{{{drawing(400,400,-2,2,-2,2, circle(0,0,sqrt(2)),rectangle(-1,-1,1,1),
locate(0,-1,8cm),locate(1.05,0,8cm)

 )}}}

Draw a diagonal of the square (in green):

{{{drawing(400,400,-2,2,-2,2, circle(0,0,sqrt(2)),rectangle(-1,-1,1,1),
locate(0,-1,8cm),locate(1.05,0,8cm), green(line(-1,-1,1,1))

 )}}}

That green diagonal is a diameter of the circle, and its length can
be calculated using the Pythagorean theorm on the right triangle which
is the lower half of that square.

a² + b² = c²
8² + 8² = c²
64 + 64 = c²
    128 = c²
   &#8730;<span style="text-decoration: overline">128</span> = c
  &#8730;<span style="text-decoration: overline">64·2</span> = c
    8&#8730;<span style="text-decoration: overline">2</span> = c

So the diameter of the circle is 8&#8730;<span style="text-decoration: overline">2</span>cm

The formula for the circumference of a circle is

C = <font face="symbol">p</font>d where d is the diameter.

C = <font face="symbol">p</font>·8&#8730;<span style="text-decoration: overline">2</span>

C = 8<font face="symbol">p</font>&#8730;<span style="text-decoration: overline">2</span>.

That's approximately 35.543 cm.


Edwin</pre>