Question 764792
{{{drawing( 400, 400, -15, 15, -15, 15,red(circle( 0, 0, 12 )), line(12,0,6,6*sqrt(3)), line(6,6*sqrt(3),-6,6*sqrt(3)), line(-6,6*sqrt(3),-12,0), line(-12,0,-6,-6*sqrt(3)),line(-6,-6*sqrt(3),6,-6*sqrt(3)), line(6,-6*sqrt(3),12,0),blue(line(0,0,-6,-6*sqrt(3))),blue(line(0,0,6,-6*sqrt(3))) ,locate(-3,-5,"12"),locate(1.5,-5,"12"), locate(-1,-9,"12"))}}}
An equilateral triangle is formed by joining the two radii (color blue) and the side of an inscribed hexagon.
Since the radius is 12 cm, then each side of a hexagon measures 12 cm.
The perimeter of the hexagon is 6 times 12 cm = 72 cm.

ANSWER: 72 cm