Slicing a circle's surface area in 3 equal parts not the usual way

Question

Is there a method to slice a circle's surface area in three equal parts by slicing the circle using two straight lines whose common point of origin is located on the circumference of the circle?

Answer 1

Here you find instructions - some work left for you:

The goal is to find angle CBD. Given BC, f, the triangle ABC is well defined for a given radius. We will create an equation for f in which the section BCD of the circle will be equal to the segments under the arcs. The sector ABD ,ay be calculated as function of f - angle CAD is related to angle BAC. Angle BAC = Angle BAD. Angels BAC + BAD + CAD = 2$\pi$. Does this detailed enough?