Does the Dottie number help solve the trisection or quintisection of a disc into equal-area parts by chords coming from a point on the circumference?

Question

Since the problem of quartisection of a disc into four parts of the same area by chords coming from the same point can be solved via Dottie number as shown on this picture:

I wonder, whether the problems of trisection and quintisection of disc also can be solved using Dottie number.