Question 353183
{{{drawing (300,300,-10,10,-10,10,green(arc(0,0,12,12,0,270)),circle(0,6,0.3),circle(6,0,0.3),circle(0,0,0.3),locate(-2,3,R),locate(3,-1,R),locate(4,4,H),line(0,0,0,6),line(0,0,6,0),blue(line(0,6,6,0)))}}}
The circumference of a circle is,
{{{C=pi*D}}}
{{{pi*D=12*pi}}}
{{{D=12}}}
If we looked at the circle on a coordinate system, the one endpoint would be at ({{{R}}},{{{0}}}) and the other would be at ({{{0}}},{{{R}}}), where {{{R}}} is the radius of the circle.
The shortest distance between two points in Euclidean geometry is a straight line.
The two points and the origin also desribe an isoceles right triangle with equals length sides of {{{R}}}. 
You can use the Pythaogorean theorem to find the hypotenuse.
{{{R^2+R^2=H^2}}}
{{{H^2=2R^2}}}
{{{H=sqrt(2)*R}}}
{{{H=sqrt(2)*(D/2)}}}
{{{H=sqrt(2)*6}}}
{{{highlight(H=6*sqrt(2))}}}