Question 955620
{{{drawing(200,200,-1.3,1.3,-1.3,1.3,

rectangle(-1,-1,1,1),circle(0,0,1),
line(-1,0,0,1),line(0,1,1,0),line(1,0,0,-1),line(0,-1,-1,0),
locate(.5,1.2,S),locate(1.05,.6,S)


 )}}}

Adding those 4 tangents to the circle merely circumscribes a
larger square around the circle, and if you draw the diagonals of the
inner (smaller ) square, you see that S is also the radius of the
circle:

{{{drawing(200,200,-1.3,1.3,-1.3,1.3,

rectangle(-1,-1,1,1),circle(0,0,1),
triangle(-1,0,1,0,0,1), triangle(-1,0,1,0,0,-1),
triangle(-1,0,0,1,0,-1), triangle(1,0,0,-1,0,1),
locate(.5,1.2,S),locate(1.05,.6,S),
locate(.45,0,S)
  )}}}

and since the circlumference of a circle is given by

C = 2<font face = "symbol">p</font>r, and since the radius

is S, we substitute S for r and get

C = 2<font face = "symbol">p</font>S

Edwin</pre>