Find the side of the inscribed 12-gon in a circle with a radius of 20m.

We have a circle circumscribed around a polygon, the radius of a circle circumscribed around a regular polygon is:
R = a / (2 * sin (180 / n)), where a is the side of the polygon, n is the number of corners of the polygon.
Let us express from this expression the length of the side of the polygon:
a = R * 2 * sin (180 / n)
We have, by condition, n = 12.
We get:
a = R * 2 * sin (180 / n) = 20 * 2 * sin (15)
According to the Bradis table, we find that the sine is 15, equal to 0.258
Find the side of the polygon:
a = 20 * 2 * sin (15) = 20 * 2 * 0.258 = 10.32 cm.
Answer: The side of the polygon is 10.32 cm.