Divide the area of a circle in 3 equal parts starting from a point on the circle

Question

I'm asking for your help or a hint on whether there is a method to divide a circle's area in three equal parts starting the slicing by a point on the circumference of the circle.

Answer 1

Connect the point on the circumference to the origin, then calculate an angle of $120$ degrees in any direction, then slice along that angle. Slice back to the origin, repeat in the same direction as before.

Answer 2

Your task can be divided into two steps.

1. Determine the center of the circle
2. Connect the center to an arbitrary point on the circle circumference. Then construct an equilateral triangle on this connection. Then construct an additional triangle on the inner edges of the triangle. This will create a 120° angle repeat the same procedure to get a 240° angle and you are done.