Comments from Askold:

Urgent: add converse of Ceva's theorem! (seems to be done)

Correction: Ceva's theorem is wrong: either the lines intersect at one point or they are parallel.

In the relationship between Menelaus' theorem and Ceva's theorem one can add discussion of harmonic quadruples of points. Perhaps one can discuss this in the chapter on projective geometry.

Comments from fofx:

Is exercise 4 from problem set 1 still valid even if the given triangle is regular triangle?
problemset1exercise4.png