If you measure the radius, then start from a point on the circumference, and set off a chord (a straight line that touches the circumference at both ends, equal to the radius, and from the end of that chord set off another one, the end of the second chord will be on a point 1/3 of the circumference.
Old guy
How about measuring the circumference, dividing by 3 and marking the circumference by the result. Draw a line to the center from those 3 points.